Method and Apparatus for Measurement of Material Condition

ABSTRACT

System and method for characterizing material condition. The system includes a sensor, impedance instrument and processing unit to collect measurements and assess material properties. A model of the system may be used to enable accurate measurements of multiple material properties. A cylindrical model for an electromagnetic field sensor is disclosed for modeling substantially cylindrically symmetric material systems. Sensor designs and and data processing approaches are provided to focus the sensitivity of the sensor to localize material conditions. Improved calibration methods are shown. Sizing algorithms are provided to estimate the size of defects such as cracks and corrosion. Corrective measures are provided where the actual material configuration differs from the data processing assumptions. Methods are provided for use of the system to characterize material condition, and detailed illustration is given for corrosion, stress, weld, heat treat, and mechanical damage assessment.

This application is a continuation of U.S. patent application Ser. No.15/030,094, filed Apr. 18, 2016 which itself is a continuation ofInternational Application No. PCT/US2014/061825 with an internationalfiling date of Oct. 22, 2014, which itself claims priority under 35U.S.C. § 119(e) to U.S. provisional patent application, U.S. Ser. No.61/894,191, filed Oct. 22, 2013, and U.S. provisional patentapplication, U.S. Ser. No. 62/009,771, filed Jun. 9, 2014, all of whichare herein incorporated by reference in their entirety.

BACKGROUND

Inspection of material condition is an important aspect of costeffective maintenance of high value assets (such as aircraft, trains,and other vehicles; transportation infrastructure; refineries,pipelines, other oil and gas infrastructure, to name a few). Majorfactors driving inspection costs include the cost of the equipment, theamount of time it takes to perform the inspection, the amount ofdisassembly required to perform the inspection, the cost of reassembly(or repair if the inspection is destructive), and the expertise andnumber of required operators.

Defects of interest vary by application, and include cracks, fatigue,corrosion, stress corrosion crack colonies, inclusions, pits, dents,gauges, corrosion-fatigue, cracks in dents, and other combinations ofdefects and other defects caused by service, manufacturing, or otherevents and processes.

A variety of sensor technologies have been developed to support theinspection needs of industry. Electromagnetic methods for inspectioninclude Radiography, eddy-current testing (ET), Magnetic Flux Leakage(MFL), Magnetic Particle Testing (MPT or MT), Electromagnetic AcousticTransmission (EMAT) and other variations on these and other methods.

In general, for advanced ET methods transimpedance is measured asindicated in FIG. 3. A signal generator 112 creates a sinusoidalwaveform signal. This signal is applied to the system being tested, inthis example, sensor 120. Multiplier 114-A multiplies the output ofsensor 120 with the original signal and the result is passed through alow pass filter (LPF) 114-B to eliminate all frequency components exceptzero. The output of the filter is the real component of thetransimpedance. To obtain the imaginary (90° phase) component, thereference signal used in the multiplication is shifted by 90°.

Multiplication and low-pass filtering is accomplished with electronicsoperating on the analog signal output from signal generator 112 andsensor 120. The output of LPF 114-B may be converted by an analog todigital converter for later processing or presentation on a digitaldisplay. There is a certain length of time that needs to pass betweenthe time the signal is applied and a valid measurement can be taken, dueto settling time of LPF 114-B.

SUMMARY

Some embodiments relate to an impedance instrument comprising a signalgenerator and a sensing channel. The signal generator is configured togenerate an in-phase reference signal, a quadrature reference signal,and an electrical signal oscillating at a first excitation frequency,wherein the in-phase reference signal is a digital precursor to theelectrical signal, and the quadrature reference signal is a version ofthe in-phase reference signal shifted one-quarter period. The sensingchannel has an analog-to-digital converter to digitize a response signaland a module to process successive digitized samples of the digitizedresponse signal with each of the in-phase and quadrature referencesignals, to produce an impedance measurement.

The in-phase reference signal may have the same phase as the electricalsignal. The sensing channel may be among a plurality of parallel sensingchannels each having a respective module configured to simultaneouslyprocess a respective digitized response signal with the in-phasereference signal and quadrature reference signal.

The module may be configured to simultaneously process the successivedigitized samples of the digitized response signal by independently atleast multiplying the digitized samples by the in-phase and quadraturereference signals. The module of the sense channel may be implemented asa field-programmable gate array (FPGA). The module may produce a realpart of the impedance measurement from the digitized samples processedwith the in-phase reference signal, and the module produces an imaginarypart of the impedance measurement from the digitized samples processedwith the quadrature reference signal.

The signal generator may be further configured to generate theelectrical signal such that the electrical signal additionallyoscillates at a second excitation frequency. The signal generator mayalso in-phase and quadrature reference signals at the second frequency.

In some embodiments, the impedance instrument further comprises acombiner module may be configured to add the first and second in-phasereference signal into a single combiner output signal. The combinermodule is further configured to apply a separate weight to the first andsecond in-phase reference signals before adding.

The processing of the successive digital samples by the module mayinclude multiplying the successive digital samples by correspondingsamples of the in-phase reference signal and adding the result to afirst running sum; and multiplying the successive digital samples bycorresponding samples of the quadrature reference signal and adding theresult to a second running sum.

The impedance instrument may include a non-transient computer storagemedium storing a database of precomputed impedances for a sensor andtest object; and a processor configured to receive the impedancemeasurement from the sensing channel and process the impedance with thedatabase to determine a property of the test object.

Some embodiments are directed to a method of operating the impedanceinstrument of claim A1. The method may comprise acts of operablyconnecting the impedance instrument to a sensor; placing the sensorproximal to a surface of a test object coated with a coating; excitingthe electrical signal into the sensor using the signal generator,wherein a skin depth at the first excitation frequency is greater than athickness of the coating; measuring the impedance with the sensingchannel, the impedance having a phase of less than 1 degree; andprocessing the impedance measurement to determine a property of the testobject.

In some embodiments of the method, the sensing channel is among aplurality of identical sensing channels, the sensor comprises aplurality of sensing elements, operably connecting the impedanceinstrument to the sensor comprises connecting each of the plurality ofsensing channels to a respective sensing element, the measuring of theimpedance is performed on each of the plurality of sensing channels, andthe processing is performed to each of the impedance measurements toproduce an image of the property of the test object.

In some embodiments the test object is a biological material and themethod further comprises assessing health of the biological materialbased on the property. The biological material may be a brain and theproperty may be a condition of the brain. The property may be damage tothe test object and the method may further comprise quantifying thedamage. The property may be a temperature of a subsurface location inthe test object. The property may be moisture ingress into the testobject. The property may be moisture ingress and the image may be a mapindicating susceptibility to corrosion.

The acts of exciting, measuring and processing may be repeated at aplurality of times, and changes in the property may be monitored overtime. The sensor may be maintained in a fixed position relative to thetest object throughout the repetitions.

The measuring act may include performing a plurality of impedancemeasurements on each sensing channel and scanning the sensor across thecoated surface of the test object during measuring.

Some embodiments are directed to a method of measuring impedance. Themethod may include generating a digital, in-phase reference signal and adigital, quadrature reference signal, the quadrature reference signal isa version of the in-phase reference signal shifted one-quarter period;providing an electrical signal oscillating at a first frequency to adevice having two or more ports, the electrical signal having beengenerated based on the in-phase reference signal; digitizing a responsesignal from the device; processing digitized samples of the responsesignal with the in-phase reference signal to measure a first componentof the impedance; processing the digitized samples of the responsesignal with the quadrature reference signal to measure a secondcomponent of the impedance; and providing the first and second componentof the impedance as a representation of the impedance of the device.

The device may be a sensor, such as an eddy current sensor or amagnetoresistive sensor.

Impedance may be represented in complex form having a real and animaginary part, and the first component of the impedance is the realpart, and the second component of the impedance is the imaginary part.

Another aspect relates to an impedance instrument having a signalgenerator and a sense channel. The signal generator may have a referencesignal generator, a combiner, and a module. The reference signalgenerator is configured to generate a reference signals at a pluralityof frequencies, each frequency having an in-phase reference signal and aquadrature reference signal, the quadrature reference signal being aversion of the in-phase reference signal shifted one-quarter period. Thecombiner to generate a combined signal by applying a weight to eachin-phase reference signal and adding the weighted in-phase referencesignals. The module is configured to generate and output an excitationsignal by at least amplifying the combined signal. The sense channel hasan analog to digital converter and a multiply/accumulate module. The ADCdigitizes a response signal into n successive digitized samples. Themultiply/accumulate module to separately multiply the n successivedigitized samples by respective samples of respective reference signals,to separately add products of the multiply associated with eachreference signal, and divide each total by n to produce compleximpedance measurements at each of the plurality of frequencies.

Another aspect relates to a system for estimating properties from sensormeasurements. The system has a sensor, a calibration module, animpedance analyzer, a MIM module, and a recalibration module. Theimpedance analyzer measures raw impedance data from the sensor. Thecalibration module is configured to calibrate the raw impedance datausing reference data. The MIM module is configured to use a multivariateinverse method to generate reference set properties using a referenceset of the calibrated impedance data, a precomputed database, andproperty assumptions. The recalibration module is configured torecalibrate the calibrated impedance data using the reference setproperties, producing recalibrated data. The MIM module is furtherconfigured to use the multivariate inverse method to generate estimatedproperties using the recalibrated data and the precomputed database.

The sensor may be placed proximal to a test object during measurement ofthe raw impedance data by the impedance analyzer. The reference set ofcalibrated impedance data may be acquired as raw impedance data at alocation on the test object having nominal properties, and the propertyassumptions comprise at least one of the nominal property.

The system may also include an assessment module configured to determineif the test object is acceptable based on the estimated properties. Thesystem may further include a post-processing module configured tocross-correlate a select property among the estimated properties with aknown spatial variation of said select property that results frommeasurement at a discrete flaw. The the assessment module may make theassessment based at least in part on the select property after the crosscorrelation.

The system may further include a scanner configured to hold and move thesensor along the test object as the impedance analyzer measured rawimpedance data and an encoder to record the corresponding position ofthe sensor during measurements. The impedance analyzer may record theraw impedance data with the correspond position of the sensor.

The system may further include a user interface configured to display aspatially registered image indicating an area where the test object wasdetermined to be unacceptable by the assessment module.

In some embodiments, precomputed database is generated from ananalytical model of the test object and sensor. The test object andsensor may be approximated by the analytical model as having cylindricalsymmetry. The analytical model for the sensor may include the drivewinding of these sensor, such that the drive winding has a portion thatis circumferential, having a constant radius and constant axial positionalong a center axis of cylindrical symmetry.

The test object may be a pipe having insulation and weather-jacket andthe estimated properties may include sensor lift-off, insulationthickness, and pipe wall thickness.

The sensor may have first and second arrays of sensing elements, eachelement of the first array having a respective element of the secondarray. The system may further include a preprocessing module configuredto combine calibrated impedance measurements from the respective sensingelements of the arrays prior to use of the calibrated impedance data bythe MIM module to generate the reference set.

The sensor may include an array of sensing elements and the impedanceanalyzer may measure raw impedance data at a plurality of frequenciesfor each of the sensing elements in the array.

Another aspect relates to a method of estimating properties of a testobject from raw impedance data. The method includes obtaining areference set of impedance data measured on the test object; calibratingthe reference set using calibration data; estimating calibrationproperties for the raw impedance data using the calibrated referencesubset; measuring the raw impedance data with a sensor on the testobject; calibrating the raw impedance measurements using the calibrationproperties; estimating the properties of the test object using apre-computed database.

The reference set of impedance data may be obtained using the sensor.The calibration data may be data obtained by the sensor with any testmaterials outside a range of sensitivity of the sensor. The calibrationdata may be taken on a reference part other than the test object.

Estimating the calibration properties may include applying amultivariate inverse method to the calibrated reference subset, themultivariate inverse method utilizing the precomputed database of sensorresponses and at least one property assumption for the test object.

In some embodiments, the precomputed database is a first precomputeddatabase for the properties to be estimated, and estimating thecalibration properties comprises applying a multivariate inverse methodto the calibrated reference subset, the multivariate inverse methodutilizing a second precomputed database for a subset of the propertiesto be estimated. The precomputed database may be generated from ananalytical model of the test object and sensor. The test object andsensor may be approximated by the analytical model as having cylindricalsymmetry. The analytical model for the sensor may include a drivewinding having a portion that is circumferential, having a constantradius and constant axial position along a center axis of cylindricalsymmetry. The test object may be a pipe and the sensor may havemagnetoresistive sensing elements.

The method may further comprise correlating an electrical property amongthe estimated properties with depth of a crack. The correlation may beaccomplished using a correlation relationship determined from empiricaldata on representative defects and a crack length is also determinedusing a spatial image generated from the response at multiple locationson the test object. The correlation may be accomplished using acorrelation relationship determined from computer simulated data forrepresentative defect geometries.

The crack may be among a plurality of cracks within a stress corrosioncrack colony and the depth of a deepest crack is estimated. Correlatingmay include an effect of a second crack on the electrical property. Theeffect of the second crack on the correlation may be determined using acomputer model. The computer module may be used to compute a scalefactor for the depth.

A precomputed database may be used to estimate the lift-off before andafter the crack and to determine an effective conductivity change at thecrack for all locations along the crack.

Measuring the raw impedance data may be performed with a drive windingof the sensor orientated perpendicularly to a length direction of thecrack and the sensor is moved in the direction of the crack length.Measuring the raw impedance data may performed with a drive winding ofthe sensor orientated between 30 and 60 degrees relative to a lengthdirection of the crack and the sensor is moved in the direction of thecrack length.

Another aspect relates to an inspection apparatus for determiningquality of a weld in a test object. The apparatus may include at leastone sensing segment, each sensing segment having an array of sensingelements at a fixed distance from at least one linear drive conductor;an impedance instrument having a signal generator configured to generatean electrical current at least one excitation frequency, said signalgenerator electrically connected to provide the electrical current tothe drive conductor; and a plurality of parallel sensing channels, eachsensing channel dedicated to a sensing element of the at least onesensing segment and configured to simultaneously measure real andimaginary components of an impedance associated with the respectivesensing element at each of the at least one excitation frequencies; ascanning apparatus configured to move the at least one sensing segmentrelative to the weld as the impedance instrument measures impedancesfrom the at least one sensing segment, a MIM module configured to applya multivariate inverse method to the measured impedances to determinethe magnetic permeability as a function of position in the test object,and a post-processing module configured to compute a feature of themagnetic permeability response that correlates with weld quality.

The array of sensing elements may be an array of conductive sensingloops.

The scanning apparatus may be in the form of an in-line-inspection toolfor pipeline inspection, multiple sensing arrays are included withindividual linear drive conductors on retractable arms with arcs thatmatch the internal curvature of a pipe to be inspected.

The sensing elements may be inductive and a speed of the tool varies asthe tool experiences varied pipeline elevation and the data rate isequal to a multiple of the time for a single drive current cycle at thelowest of one or more prescribed frequencies and where a precomputeddatabase of sensor responses is used to convert the response at eachsensing element into a magnetic permeability and lift-off value.

The linear drive conductor may be oriented circumferentially and themagnetic permeability provides a combined measure of both metallurgicalchanges and axial stress.

Multiple linear drive conductors may be included at equal spacing aroundthe circumference but are oriented axially to provide a measure of themagnetic permeability in the circumferential, hoop, direction.

The post-processing module may correlate the magnetic permeability withstress in the weld and the weld quality is assessed based on the tensilestresses not exceeding a prescribed limit.

The test object may comprise a pipe with a coating on the outer surface,the linear drive segment may be oriented axially and the scanningapparatus enables movement of the sensor array in the circumferentialdirection on the outer surface of coating of the pipe, and the MIMmodule may use a precomputed database to estimate the magneticpermeability in the circumferential direction.

The test object may be a pipe and the linear drive conductor may beoriented at 45 degrees relative to a central axis of the pipe so thatboth the hoop and longitudinal components of stress affect the magneticpermeability estimate and the magnetic permeability is determined usinga precomputed database of sensor responses.

Another aspect relates to a method comprising operating the inspectionapparatus of claim F1 to perform inspection of a weld before post-weldheat treatment (PWHT); heat treating the weld; and operating theinspection apparatus of claim F1 to perform inspection of a weld afterPWHT, wherein the post-processing module computes the feature of themagnetic permeability response that correlates with weld quality usinginspection results from both before and after PWHT.

The feature of the magnetic permeability computed by the post-processingmodule may be a change in a width of a response for the response afterPWHT when compared to the response before PWHT. The feature of themagnetic permeability may be a reduction in a highest local peak of themagnetic permeability near a center line of the weld after PWHT whencompared to the response before PWHT. The feature of the magneticpermeability response may be a change in difference between apermeability associated with a base material portion of the test objectand a permeability of a region within a heating coil covered regionneighboring the weld for the magnetic permeability after PWHT whencompared to the response before PWHT.

Another aspect relates to a method comprising operating the inspectionapparatus to perform inspection of a weld after post-weld heat treatment(PWHT). The method may include determining the relationship betweenmagnetic permeability and stress for the weld, a heat affected zoneproximal to the weld, and the base material of the test object byapplying stress to small coupons of representative material anddeveloping a correlation relationship between applied stress and themagnetic permeability measured with a sensor that has a similar geometryto the at least one sensing segment.

Another aspect relates to a method comprising operating the inspectionapparatus at two or more different times on the test object and using achange in response to determine if the condition of the weld hasdegraded.

Another aspect relates to a method comprising operating the inspectionapparatus of to measure magnetic permeability in two orientations, andproducing a measure of anisotropy in the magnetic permeability;assessing weld quality based on the measure of anisotropy.

Another aspect relates to an in-line inspection (ILI) tool comprising atool body; a plurality of sensing segments, each sensing segment havingan array of sensing elements and a drive conductor with an arc-shapedsegment; a plurality of armatures, each controlling retraction andprotraction of a respective sensing segment with respect to the toolbody; an impedance instrument having a signal generator configured togenerate an electrical current at a first excitation frequency, saidsignal generator electrically connected to provide the electricalcurrent to the drive conductor of each of the plurality of sensingsegments, and a plurality of parallel sensing channels, each sensingchannel dedicated to a sensing element of the plurality of sensingsegments and configured to simultaneously measure real and imaginarycomponents of an impedance associated with the respective sensingelement at the first excitation frequency; a non-transient computerstorage medium storing a precomputed database of sensor responses; and aprocessor configured to receive the impedance measurements from theimpedance instrument and determine (i) a distance between each of therespective sensing elements an internal surface of a test material and(ii) a property of the test material using at least the precomputeddatabase. The at least one sensing segments may comprises first andsecond sensing segments, and the second sensing segment may be orienteddifferently than the first.

In some embodiments, the electrical current further comprises a secondexcitation frequency, the plurality of sensing channels of the impedanceinstrument are further configured to simultaneously measure real andimaginary components of a second impedance associated with therespective sensing element at the second excitation frequency, theproperty is magnetic permeability, and the processor is furtherconfigured to determine (iii) the pipe wall thickness.

The first excitation frequency may be higher than the second excitationfrequency, and the determination of the distance may be made without useof the impedance measured at the second excitation frequency.

The property may be magnetic permeability and the tool further comprisesan ultrasonic measurement device configured to measure wall thickness,and wherein the processor utilizes the ultrasonic wall thicknessmeasurement in estimating the magnetic permeability.

The processor may be further configured to determine the conductivity ofthe test material. The conductivity may be determined by assuming anominal wall thickness value away from any defect like responses usingthe precomputed database and at least two frequencies of data. Theconductivity estimate may be assumed to be the same at all otherlocations and the magnetic permeability, wall thickness and lift-off areestimated using the responses at least two frequencies.

The impedance instrument may determine an impedance for each of theplurality of parallel sensing channels, by dividing a voltage of therespective sensing element with the electrical current on the driveconductor.

The arc shaped segment of the drive conductor may be orientedcircumferentially. The arc shaped segment of the drive conductor may beoriented between 10 and 50 degrees off of a circumferential orientation.The drive conductor may be wound in a square wave meander with thelonger segments in the axial direction

The tool may have a tether and a mechanism for allowing the gas orliquid product to flow past the tool to reduce the tool speed.

The array of each sensing segment may include two rows of sensingelements.

The test material may be a pipe. The pipe may be a pipeline.

The property may be a magnetic permeability of the test material.

The impedance instrument may measure the impedance on each of theplurality of parallel sensing channels at least 3,000 times per second.

The tool can provide lift-off correction and magnetic permeabilityimaging at variable speeds over ranges from less than 1 m/s to over 10m/s without modification and can correct for lift-off variations of over1 cm and tool tilting. The lift-off is estimated to correct the magneticpermeability and wall thickness estimates for variable lift-off using aprecomputed database. The tilt of the tool may be estimated using theresponse of sensing elements at at least two different axial positionsalong the tool from two different arc segments to provide an estimate ofthe tool tilt which is then used to correct a second property estimateusing a model. The tool may comprise a plurality of encoders, eachencoder configured to record a position of a respective armature, andwherein the processor is further configured to determine an internalsurface profile and concentricity response from the recorded encoderpositions and the determined distances of the respective sensingelements the internal surface of a test material.

Another aspect relates to a method of operating the ILI tool, the methodcomprising launching the ILI tool from a cleaning tool pipelineinspection gauge (PIG) (PIG is an acronym for “Pipeline-InspectionGauge”) launcher into a pipe; operating the tool to collect impedancedata from the plurality of sensing segments; processing the impedancedata to produce processed data, the processed data including distanceand property estimates; and retrieving the tool. The method may furtherinclude identifying a characteristic response associated with a weldfrom at least one of the distance and the property; and counting anumber of welds passed by the tool.

The property may be a magnetic permeability of the test material and themethod may further include producing a crack response from the magneticpermeability; detecting a crack from the crack response; and determininga position of the crack using a position of the tool and a location ofthe sensing element at a time the crack response was measured.

The crack may be a stress corrosion crack (SCC). The crack may be a seamweld crack. The crack response may be processed to estimate crack depth.

After launching and prior to retrieving the tool, the method may includemeasuring a first set of impedance data with the impedance instrumentwhile the tool is traveling at a speed under 1 meter per second; andmeasuring a second set of impedance data with the impedance instrumentwhile the tool is traveling at a speed over 10 meters per second. Themethod may include operating the processor to process to determine thedistance from the first set of impedance data; and operating theprocessor to process to determine the distance from the second set ofimpedance data.

The method may include, after launching and prior to retrieving thetool, operating the tool to provide a plurality of measurements of thedistance and the property while a speed of the tool within the pipevaries over 5 meters per second.

A tilt of the tool may be computed.

In some embodiments, the method includes producing a damage responsefrom at least one of the distance and the property; and estimating asize of the damage using at least the damage response.

The test material may be a pipe and the damage may be corrosion internalto the pipe. The damage may be internal and external corrosion, and thedistance may be used to differentiate the two. The damage may be, forexample, mechanical damage, hard spots, a girth weld crack, or, a seamweld crack.

The method may further include producing a post weld heat treatcondition response from at least one of the distance and the property;and estimating a quality of a post weld heat treatment to the testmaterial from at least the post weld heat treat condition response.

The method may further include estimating bending stress in the testmaterial from at least one of the distance and the property.

The method may further include comparing the processed data to earlierprocessed data; and detecting a change in condition of the test materialbased on the comparison.

The detected change in condition may be a change in corrosion, and thecorrosion growth may be quantified. The detected change in condition maybe a change in crack size, and the crack growth may be quantified. Thedetected change in condition may be used to detect cracks.

Another aspect relates to a method for detecting defects in a conductinglayer, the method comprising acts of: placing an eddy current sensorproximal to a surface of the conducting layer, the eddy current sensorhaving a driving winding and a linear array of sensing elements;exciting the drive winding with an electrical current at a firstexcitation frequency, the first excitation frequency having a depth ofpenetration between 50% and 150% of a thickness of the conducting layer;measuring a first transimpedance at the first excitation frequency foreach sensing element in the linear array of sensing elements using asingle, continuous dataset obtained from the respective sensing element;estimating a property of the thin sheet using the first transimpedance;and detecting a defect using the estimated property.

The conducting layer may be moving relative to the sensor at a speedgreater than 1 inch per second. In some embodiments, for each sensingelement the acts of measuring and estimating are repeated and theproperty is stored in association with a location on the conductinglayer. In some embodiments, a linear portion of the drive winding isspaced from the linear sensing array by a distance less than 10 timesthe thickness of the conducting layer.

In some embodiments, measuring the transimpedance comprises: multiplyingthe dataset by an in-phase reference signal; and multiplying the datasetby an quadrature reference signal.

In some embodiments, the electrical current excited in the drive windingfurther comprises a second excitation frequency higher than the first,the measuring further comprises measuring a second transimpedance at thesecond excitation frequency for each sensing element in the linear arrayof sensing elements using the single, continuous dataset obtained fromthe respective sensing element; and in the detecting, the defect isdetermined to one of a near side defect, a far side defect, or a throughwall defect.

In some embodiments, the estimating comprises: determining a lift-off ofthe sensor from the conducting layer for the sensing element using thesecond transimpedance; and determining a thickness and electromagneticproperty of the conducting layer using the first transimpedance and thelift-off.

In some embodiments, the method further comprises an act of providing astatic magnetic field near the sensor and the conducting layer, thestatic magnetic field having a magnetic field intensity within theconducting layer which causes a magnetic permeability of the conductinglayer to decrease.

In some embodiments, the method further comprises acts of placing asecond eddy current sensor having a second drive winding and secondlinear array of sensing elements proximal to an opposite surface of theconducting layer; and performing the acts of exciting and measuring withthe second eddy current sensor.

In some embodiments, the first and second eddy current sensors arespatially aligned with one another, and the drive windings are excitedwith the electrical current. In some embodiments, the electrical currentexcited in the drive windings further comprises a second excitationfrequency higher than the first, the measuring further comprisesmeasuring second transimpedances at the second excitation frequency foreach sensing element of both linear arrays of sensing elements, theestimating comprises determining lift-offs for respective sensingelements of both sensors using the respective second transimpedances,and the estimating further comprises determining the thickness of theconducting layer by subtracting the lift-offs from a known distancebetween the two sensors.

The foregoing is a non-limiting summary of the invention, which isdefined by the attached claims.

BRIEF DESCRIPTION OF DRAWINGS

In the drawings:

FIG. 1 is a block diagram of a system for inspecting a test object;

FIG. 2 is a flow diagram of method for assessing a property of a testobject;

FIG. 3 is a flow diagram for transimpedance measurement;

FIG. 4 show a sensor response to a flaw;

FIG. 5 shows a single loop drive;

FIG. 6 shows the geometry for the current stick model;

FIG. 7 shows at top structure analyzed in the case of a single drivewire and at bottom the equivalent source geometry;

FIG. 8 shows a plot of the normalized footprint contribution of asensor's magnetic field in the direction tangential to and normal to amaterial;

FIG. 9 shows a plot of normalized footprint contribution for a singleloop drive and a rectangular drive;

FIG. 10 shows the 2-D PEC model footprint for the sensor pictured inFIG. 25;

FIG. 11 shows the result when the footprint is convolved with a flawrepresentative of the one scanned in FIG. 4;

FIG. 12 shows a geometry for descrbing Love's Field EquivalencePrinciple;

FIG. 13 shows the magnitude and phase footprint of the sensor picturedin FIG. 25;

FIG. 14 shows a plot of normalized footprint contribution for animproved single loop drive and rectangular drive;

FIG. 15 shows a plot of normalized footprint contribution obtained fromthe sum of two sense elements in a double rectangular sensor;

FIG. 16 shows a flexible double row, double rectangular MR-MWM-Array;

FIG. 17 shows an improved sensor response from scanning the sensor shownin FIG. 16 over the same flaw in a flat plate as scanned in FIG. 4;

FIG. 18 shows a flow diagram of a method for constructing a sensor;

FIG. 19A shows an embodiment of an impedance analyzer;

FIG. 19B shows a flow diagram of a method for for processing datasamples;

FIG. 20 shows a flow diagram of a method for transforming “raw”impedance data obtained from an impedance analyzer into the estimateddata;

FIG. 21 shows an impedance instrument according to some embodiments;

FIG. 22 shows a plot of the relative impedance changes due to a 10%change in each material property for the CUI applications;

FIG. 23 shows the modeled eddy current sensor structure for acylindrical material;

FIG. 24 shows a cross-sectional view of the cylindrical model;

FIG. 25 shows photographs of a prototype MR-MWM Array sensor;

FIG. 26 is a plot showing that the model successfully predicts the airresponses of the sensor when wrapped around plastic cylinders of varyingdiameters;

FIG. 27 shows a plot of sensor measurements on a 6.625″ diameter, 0.25″wall thickness pipe at varying lift-offs plotted on a lift-off/thicknessgrid;

FIG. 28 shows the modeled eddy current sensor structure for acylindrical material;

FIG. 29 is a plot showing that the model successfully predicts the airresponses of the sensor when wrapped around plastic cylinders of varyingdiameters;

FIG. 30 shows a plot of sensor measurements on a 6.625″ diameter, 0.25″wall thickness pipe at varying lift-offs plotted on a lift-off/thicknessgrid;

FIG. 31 is a flow diagram of a calibration method;

FIGS. 32-36 are flow diagrams of methods of obtaining calibrationparameter values according to some embodiments;

FIG. 38 shows plots of a lattice for (top) a flaw width of 1.0 in.,(middle) a flaw length of 1.5 in., and (bottom) a flaw depth of 0.04in.;

FIG. 39 shows the maximum simulated thickness responses for various flawsizes;

FIG. 40 shows the maximum simulated thickness responses for various flawsizes;

FIG. 41 shows a flaw response from a 4″ long (circumferential), 6″ wide(axial), 0.100″ deep flaw in a 6.625″ diameter, 0.280″ thick pipe with2″ of insulation and weather jacketing;

FIG. 42 is a table showing response sizes and estimated flaw sizes;

FIG. 43 shows a sensor;

FIG. 44 shows an in-line inspection (ILI) tool;

FIG. 45 shows an ILI tool within a pipe;

FIG. 46 shows an ILI tool within a pipe;

FIG. 47 shows images of multiple scan orientations of a sensor;

FIG. 48 is a diagram showing how the distance from an ILI tool body to apipe may be estimated;

FIG. 49 is an illustration of a typical configuration of eddy currentsensors around an ILI tool body;

FIG. 50 is an illustration of an example of a sensor that has a singledrive winding and a single sense element;

FIG. 51 shows a dual rectangle drive conductor and an array of senseelements;

FIG. 52 shows an ILI tool with a circumferential drive;

FIG. 53 is a flow diagram of a process for estimating the conductivityof the pipe;

FIG. 54 is a flow diagram of a method of estimating pipe wall thickness;

FIG. 55 shows a cross-section near a girth weld joining two pipesections;

FIG. 56 shows a representative scan image of the effective permeability,obtained by processing the sensor responses through apermeability/lift-off measurement grid for an infinite half-space ofmaterial;

FIG. 57 shows an impedance view of a permeability/lift-off measurementgrid and eddy current sensor array data at two lift-offs;

FIG. 58 shows representative B-scan plots of responses for severalsensor channels that were in or near the scan path for the deepestnotches on a schedule 80 pipe;

FIG. 59 shows a representative correlation curve between the effectivepermeability change and EDM notch depth for the MWM-Array drive windingoriented perpendicular to the notch length and the permeability versusdepth correlation curves obtained with an FA24 MWM-Array sensor orientedat a 45° orientation;

FIG. 60 shows representative depth/lift-off measurement grids and datafrom schedule 40 and schedule 80 pipe;

FIG. 61 shows representative scan images of the effective permeabilityover the surface of the pipe and the depth estimate image;

FIG. 62 shows a system for inspecting a thin sheet of conductingmaterial;

FIG. 63 shows a system for inspecting a thin sheet of conductingmaterial with sensors above and below the conducting sheet;

FIG. 64 is a plot showing the depth of penetration as a function offrequency for several characteristic sensor lengths and materials;

FIG. 65 shows sensor arrays configured to inspect a thin sheet;

FIG. 66 is an illustration of a sensor in proximity of a conductingsheet; and

FIG. 67 is an illustration of sensors on opposite sides of and inproximity to a conducting sheet.

DETAILED DESCRIPTION

Section A: System Overview

FIG. 1 is a block diagram of a system 100 for inspecting a test object130. System 100 includes an instrument 110 and a sensor 120. Instrument110 is configured to provide excitation signals 121 to sensor 120 andmeasure the resulting response signals 123 of sensor 120. Measuredresponse signals 123 may be measured and processed to estimateproperties of interest, such as electromagnetic properties (e.g.,conductivity, permeability, and permittivity), geometric properties(e.g., thickness, sensor lift-off), material condition (e.g., fault/nofault), or any other suitable property or combination thereof. (Sensorlift-off is a distance between the sensor and the closest surface of thetest object for which the sensor is sensitive to the test object'selectrical properties.)

Instrument 110 may include a processor 111, a user interface 113, memory115, an impedance analyzer 117, and a network interface 119. Though, insome embodiments of instrument 110 may include other combinations ofcomponents. While instrument 110 is drawn as a single block, it shouldbe appreciated that instrument 110 may be physically realized as asingle “box”; multiple, operably-connected “boxes”, or in any othersuitable way. For example, in some embodiments it may be desired toprovide certain components of instrument 110 as proximal to sensor 120as practical, while other components of instrument 110 may be located atgreater distance from sensor 120.

Processor 111 may be configured to control instrument 110 and may beoperatively connected to memory 115. Processor 111 may be any suitableprocessing device such as for example and not limitation, a centralprocessing unit (CPU), digital signal processor (DSP), controller,addressable controller, general or special purpose microprocessor,microcontroller, addressable microprocessor, programmable processor,programmable controller, dedicated processor, dedicated controller, orany suitable processing device. In some embodiments, processor 111comprises one or more processors, for example, processor 111 may havemultiple cores and/or be comprised of multiple microchips.

Memory 115 may be integrated into processor 111 and/or may include“off-chip” memory that may be accessible to processor 111, for example,via a memory bus (not shown). Memory 115 may store software modules thatwhen executed by processor 111 perform desired functions. Memory 115 maybe any suitable type of non-transient computer-readable storage mediumsuch as, for example and not limitation, RAM, a nanotechnology-basedmemory, one or more floppy disks, compact disks, optical disks, volatileand non-volatile memory devices, magnetic tapes, flash memories, harddisk drive, circuit configurations in Field Programmable Gate Arrays(FPGA), or other semiconductor devices, or other tangible, non-transientcomputer storage medium.

Instrument 110 may have one or more functional modules 109. Modules 109may operate to perform specific functions such as processing andanalyzing data. Modules 109 may be implemented in hardware, software, orany suitable combination thereof. Memory 115 of instrument 110 may storecomputer-executable software modules that contain computer-executableinstructions. For example, one or more of modules 109 may be stored ascomputer-executable code in memory 115. These modules may be read forexecution by processor 111. Though, this is just an illustrativeembodiment and other storage locations and execution means are possible.

Instrument 110 provides excitation signals for sensor 120 and measuresthe response signal from sensor 120 using impedance analyzer 117.Impedance analyzer 117 may contain a signal generator 112 for providingthe excitation signal to sensor 120. Signal generator 112 may provide asuitable voltage and/or current waveform for driving sensor 120. Forexample, signal generator 112 may provide a sinusoidal signal at one ormore selected frequencies, a pulse, a ramp, or any other suitablewaveform.

Sense hardware 114 may comprise multiple sensing channels for processingmultiple sensing element responses in parallel. Though, otherconfigurations may be used. For example, sense hardware 114 may comprisemultiplexing hardware to facilitate serial processing of the response ofmultiple sensing elements. Sense hardware 114 may measure sensortransimpedance for one or more excitation signals at on one or moresense elements of sensor 120. It should be appreciated that whiletransimpedance (sometimes referred to simply as impedance), may bereferred to as the sensor response, the way the sensor response isrepresented is not critical and any suitable representation may be used.In some embodiments, the output of sense hardware 114 is stored alongwith temporal information (e.g., a time stamp) to allow for latertemporal correlation of the data.

Sensor 120 may be an eddy-current sensor, a dielectrometry sensor, anultrasonic sensor, or utilize any other suitable sensing technology orcombination of sensing technologies. In some embodiments, sensor 120 isan eddy-current sensor such as an MWM®, MWM-Rosette, or MWM-Array sensoravailable from JENTEK Sensors, Inc., Waltham, Mass. Sensor 120 may be amagnetic field sensor or sensor array such as a magnetoresistive sensor(e.g., MR-MWM-Array sensor available from JENTEK Sensors, Inc.), halleffect sensors, and the like. In another embodiment, sensor 120 is aninterdigitated dielectrometry sensor or a segmented field dielectrometrysensor such as the IDED® sensors also available from JENTEK Sensors,Inc. Sensor 120 may have a single or multiple sensing and driveelements. Sensor 120 may be scanned across, mounted on, or embedded intotest object 130.

In some embodiments, the computer-executable software modules mayinclude a sensor data processing module, that when executed, estimatesproperties of the component under test. The sensor data processingmodule may utilize multi-dimensional precomputed databases that relateone or more frequency transimpedance measurements to properties of testobject 130 to be estimated. The sensor data processing module may takethe precomputed database and sensor data and, using a multivariateinverse method, estimate material properties. Though, the materialproperties may be estimated using any other analytical model, empiricalmodel, database, look-up table, or other suitable technique orcombination of techniques.

User interface 113 may include devices for interacting with a user.These devices may include, by way of example and not limitation, keypad,pointing device, camera, display, touch screen, audio input and audiooutput.

Network interface 119 may be any suitable combination of hardware andsoftware configured to communicate over a network. For example, networkinterface 119 may be implemented as a network interface driver and anetwork interface card (NIC). The network interface driver may beconfigured to receive instructions from other components of instrument110 to perform operations with the NIC. The NIC provides a wired and/orwireless connection to the network. The NIC is configured to generateand receive signals for communication over network. In some embodiments,instrument 110 is distributed among a plurality of networked computingdevices. Each computing device may have a network interface forcommunicating with other the other computing devices forming instrument110.

In some embodiments, multiple instruments 110 are used together as partof system 100. Such systems may communicate via their respective networkinterfaces. In some embodiments, some components are shared among theinstruments. For example, a single computer may be used control allinstruments.

A fixture 140 may be used to position sensor 140 with respect to testobject 130 and ensure suitable conformance of sensor 120 with testobject 130. Fixture 140 may be a stationary fixture, manuallycontrolled, motorized fixture, or a suitable combination thereof. Forscanning applications where fixture 140 moves sensor 120 relative totest object 130, it is not critical whether sensor 120 or test object130 is moved, or if both are moved to achieve the desired scan.

Fixture 140 may have one or more motors 141 that are controlled bymotion controller 118. Motion controller 118 may control fixture 140 tomove sensor 120 relative to test object 130 during an inspectionprocedure. Though, in some embodiments, relative motion between sensor120 and test object 130 is controlled by the operator directly (e.g., byhand).

Regardless of whether motion is controlled by motion controller 118 ordirectly by the operator position encoders 143 of fixture 140 and motionrecorder 116 may be used to record the relative positions of sensor 120and test object 130. This position information may be recorded withimpedance measurements obtained by impedance instrument 117 so that theimpedance data may be spatially registered.

System 100 may be used to perform a method 200 for assessing a propertyof a test object, shown in FIG. 2.

At step 201 a precomputed database of sensor response signals isgenerated. The response signals generated may be predictions of theresponse signal 123 in FIG. 1 for a given excitation signal 121, sensor120 and test object 103. Response signals may be generated for a varietyof excitation signals, sensors/sense elements, and test objects,including variation in the position and orientation of the sensor andtest objet. For example, the precomputed database may be generated formultiple excitation frequencies, multiple sensor geometries, multiplelift-offs, and multiple test object properties (e.g., geometricvariations, electromagnetic property variations). The precomputeddatabase may be generated using a model of the system, empirical data,or in any suitable way. In some embodiments the model is an analyticalmodel, a semi-analytical model, or a numeric (e.g., finite element)model.

At step 203, sensor data is acquired. The sensor data may be acquired,for example, using instrument 110. Sensor data may be a recordedrepresentation of the response signal 123, excitation signal 121, orsome combination of the two (e.g., impedance). In some embodiments,sensor data is acquired at a plurality of excitation frequencies,multiple sensors (or sensing elements), and/or multiple sensor/testobject positions/orientations (e.g., as would be the case duringscanning).

At step 205, the sensor data is processed using the precomputed databasegenerated at step 201. A multivariate inverse method may be used toprocess the sensor data with the

At step 207, a property of the test object is assessed based on theprocessing of the measurement data at step 205. The property assessedmay be an electromagnetic property, geometric property, state,conditions, or any other suitable type of property. Specific propertiesinclude, for example and not limitation, electrical conductivity,magnetic permeability, electrical permittivity, layer thickness, stress,temperature, damage, age, health, density, viscosity, cure state,embrittlement, wetness, and contamination. Step 207 may include adecision making where the estimated data is used to choose between a setof discrete outcomes. Examples include pass/fail decisions on thequality of a component, or the presence of flaws. Another example it maybe determined whether the test object may be returned to service,repaired, replaced, scheduled for more or less frequent inspection, andthe like. This may be implemented as a simple threshold applied to aparticular estimated property, or as a more complex algorithm.

By performing step 201 prior to step 205 it may be possible that steps203, 205 and 207 may be performed in real-time or near-real-time.Though, in some embodiments, step 201 may be performed after step 203such as may be the case when database generation was not possible priorto the acquisition of measurement data, and perhaps further exacerbatedby the fact that the test object may be no longer available formeasurement.

Having described method 200 it should be appreciated that in someembodiments the order of the steps of method 200 may be varied, not allsteps illustrated in FIG. 2 are performed, additional steps areperformed, or method 200 is performed as some combination of the above.While method 200 was described in connection with system 100 shown inFIG. 1, it should be appreciated that method 200 may be performed withany suitable system.

Section B: Detail of Sensor

Sensor Footprint Model and Application

Motivation

After testing an initial prototype MR-MWM Array sensor pictured in FIG.25 on flat steel plates with manufactured defects at 2″ of lift-off, itbecame immediately obvious that the issue of detecting localized defectshad not been solved. FIG. 4 displays the result that motivated thefollowing model derivation.

The flat plate that was scanned had a 0.150″ deep, 3″ diameter defectetched into a 0.250″ inch steel plate. The sensor that was used had asingle rectangular drive whose conductors were 4.5″ apart,center-center. The sense elements were 1.5″ away from one of theconductors. This type of drive construct is very common in applicationsfor eddy current sensors, specifically MWM-Arrays, and it seemed like areasonable place to start.

The dark circle represents the expected location of the response whenthe sense element array was centered over the flaw. Instead, the singleuniform flaw created two responses, the largest of which was only 0.025″deep, considerably less than the 0.150″ flaw depth. Based on the spacingof the two responses, it seems that the two peaks occurred when each ofthe drive conductors were centered over the flaw. Overall, the resultshowed that the reported size and depth were not representative of thedefect, and that general sensitivity to local defects was low.

Conjecturing that the sensor's flaw response is a function of the volumeof a flaw, if this flaw provided a 0.025″ response, then we couldextrapolate that the desired 0.050″ deep, 2″ diameter defect would onlyprovide a 0.0037″ response. While this may be at the very edge of thesensor's capability, it was clear that designing a sensor with a highersensitivity to local defects was required to reliably meet or surpassthe goal of detecting 2 inch diameter 20% wall loss defects.

Based on this observation, it was hypothesized that the flaw responsecould be resolved into a single peak with a larger magnitude by using asingle drive wire that wrapped around the entire circumference of thepipeline (taking advantage of the cylindrical geometry of the targetapplication). This was a promising idea which turned out to be verydifficult to manufacture because of the requirement to solder the 80individual wires in a specified pattern at the seam. A prototype wasbuilt, and it is displayed in FIG. 5.

Unfortunately, while the response did not display two distinct peakslike the response of the initial prototype sensor, the response was muchwider than expected and of a much lower magnitude. And, the sensor wasmuch more sensitive to the ends of the pipe, over a much largerdistance. This result makes sense if we think of the sensor as providingan average thickness response over its sensor “footprint.” By movingfrom the single rectangular sensor with two conductors, to a singleconductor wrapped around the circumference of the pipe, we made thesensor footprint much larger. This was the opposite of the desiredeffect.

Therefore, it was clear based on these experiments that a model wasneeded to predict the footprint of a sensor given different driveconstructs. The following describes Methods AAA, BBB, and CCC formodeling an eddy current sensor's footprint when interacting with a testobject. It discusses their relative successes and shortcomings, andshows how the models helped to design a much more effective MR-MWM-Arrayfor the CUI application and could be applied to other eddy currentsensor designs.

Method AAA: 1-D Perfect Electrical Conductor (PEC) Footprint Model

Method AAA was for the purpose of gaining some rough intuition of thefootprint effect. It is a very simple 1-D model. The assumptions were asfollows:

The test object is a perfect electrical conductor (PEC), with σ=∞.

The drive conductors are infinitely long and infinitely thin wiresparallel to the test object at a height h from the test object.

The sense element is in the same plane as the drive conductors, also ata height h and considered to be infinitely long in the directionparallel to the drive.

FIG. 7 (top) shows the analyzed structure for the case of a single drivewire. The advantages of these assumptions are immediately evident. Themagnetic fields due to infinitely long wires above a PEC are easilycalculated using image theory. And the principle of superposition can beused to calculate the field for each drive wire independently with theentire sensor's response being the sum of the responses for theindividual drive wires.

The following analyis provides a first-order approximate representationof the sensor response to the test object as a function of position onthe material. Assuming the test object is a PEC ignores magneticdiffusion and frequency related effects; assuming that the drive isconstructed of infinitely thin line currents ignores the effect ofwinding thickness. Furthermore, since everything is considered infinitein the direction of the drive conductors, this formulation only analyzesthe footprint in the direction orthogonal to the drive conductors.Despite being so simplified, this model was very predictive of a givensensor-geometry's response to localized defects and was a good firstiteration for developing intuition on a given sensor-geometry'smeasurement footprint.

There are two analysis steps associated with this model. The first stepis a calculation of the nominal current distribution flowing along thesurface of the test material. The second step is to relate the localsurface current density to the field that would be generated in thevicinity of a sense element. This is used to determine the sense elementresponse to a local feature (i.e., material loss that leads to areduction in the surface current) anywhere in the vicinity of the drivewinding and provides the sensor response footprint.

The basic geometry for a single wire is shown in FIG. 7 (top). It isassumed that the drive winding carries a current I out of the page (inthe {circumflex over (z)} direction) and is located at an x position ofw and a y position of h. The sense element is also located at a height habove the surface of the test material.

Assuming that the test material is a PEC, the test material can bereplaced with an image current source (this is equivalent to assumingthat the excitation frequency is relatively high compared to the eddycurrent skin depth in the test material). This allows the magnetic fieldabove the test material to be determined, which, in turn, allows theinduced eddy current surface distribution in the test material to bedetermined. Using the equivalent source geometry of FIG. 7 (bottom), themagnetic field intensity just above the surface of the test material canbe obtained from the Biot-Savart law as

$\begin{matrix}{{H(s)} = {\frac{1\;}{\pi}\frac{h}{h^{2} + ( {x - w} )^{2}}\hat{x}}} & (4.1)\end{matrix}$

The current flowing through the surface of the test material is thendetermined from the boundary condition that requires the tangentialcomponent of the field intensity H_(x) to be zero inside the testmaterial. This surface current density can be expressed as

$\begin{matrix}{{K(x)} = {{\hat{y} \times H_{x}\hat{x}} = {\frac{1\;}{\pi}\frac{h}{h^{2} + ( {x - w} )^{2}}\hat{z}}}} & (4.2)\end{matrix}$

The second step is to project this local current density back to thelocation of the sense element so that the field that would be measuredby the sense element can be determined. In air, without a test materialpresent, the field intensity in the vicinity of the sense element is

$\begin{matrix}{{H_{air}(x)} = {{- \frac{I}{2\; \pi \; w}}\hat{y}}} & (4.3)\end{matrix}$

This field is perturbed from the air response by the presence of thetest material. Using the same Biot-Savart law given above, theperturbation in the field around the sense element due to the inducedsurface current is

$\begin{matrix}{{{dH}(x)} = {{\frac{I\; \Delta \; x}{2\pi^{2}}\lbrack \frac{h}{h^{2} + ( {x - w} )^{2}} \rbrack}\lbrack \frac{{{- h}\hat{x}} + {x\hat{y}}}{h^{2} + x^{2}} \rbrack}} & (4.4)\end{matrix}$

where Δx is the incremental spacing in the {circumflex over (x)}direction. The first term in brackets comes from the imposed field whilethe second term comes from the projection of the surface current back tothe sense element. This formulation provides both components of themagnetic field at the sense element. In general, the MR-MWM-Array isonly sensitive to the normal component (ŷ component) of the magneticfield. This is because there is no tangential component of the fieldwhen measuring in air, which makes an air calibration of this componentmore difficult. It would be accurate to classify the tangentialcomponent sensor as a differential sensor with respect to the testobject.

One very interesting product of this analysis was proving that thedifferent components of the magnetic field have very differentfootprints. For example, as shown in FIG. 8, a sensor detecting thecomponent of the field tangential to the material would have a largerpeak response to a local defect with different shaped sidelobes. Thepotential advantages of these two factors will be discussed in thefollowing section on sensor optimization. Sensing the tangential fieldwould also reduce the sensor's response to air, allowing the sensor tobe driven with more current without saturating the sensor's response. Asmentioned above, a different calibration routine would be necessary forthe tangential sensor.

The tangential sensor footprints are also examined in Method's BBB andCCC although their results are not discussed.

Calculating the footprints of the single loop drive pictured in FIG. 5and a the rectangular drive shown in FIG. 25 demonstrates the validityof this approach. These footprints are very representative of themeasurements taken and are shown in FIG. 9. The footprints arenormalized by the area under the footprint curve to show the relativesensitivity to the material as a function of position. Despite thesimplicity of the analysis, the footprint of the rectangular drivepredicts the two response peaks at 4.5″ apart. Furthermore the footprintmodel predicts a wider, single peak for the single loop drive.

Because of the inital success of the 1-D PEC analysis, the model wasextended to take into consideration the finite length of the drive andsense elements as well as drive wires of finite thickness. This resultsin a calculation of a 2-D PEC footprint which can be used to provideinitial predictions in sensor sensitivity. This model is derived in thefollowing.

Method BBB: 2-D PEC Footprint Model

The basic approach for the 2-D PEC footprint model, Method BBB, is thesame as the 1-D PEC footprint model: first determine the current densityinduced on the surface of the PEC and then reflect that back to themagnetic field at the location of the sense element. The main differenceis that instead of an infinitely long and thin current wire over thePEC, we have a discrete current volume, representing a finite wire withwidth and length.

This problem can be formulated conveniently by the “current stick model”[H. Haus, J. Melcher, Electromagnetic Fields and Energy, Prentice-HallInc., New Jersey, 1989.]. The geometry for this model is shown in FIG.6. The model uses the Biot-Savart law to derive:

$\begin{matrix}{{H(r)} = {\frac{j}{4\pi}\frac{c \times a}{{{c \times a}}^{2}}( {\frac{a \cdot c}{c} - \frac{a \cdot b}{c}} )}} & (4.5)\end{matrix}$

The current volume can then be approximated as an integral, or moreconveniently implemented in Matlab as a Riemann-Sum, where eachsub-volume's current is considered to concentrated in a current-stick atthe sub-volume's center. Therefore, as in the 1-D case, we can then useimage theory to calculate the induced surface current density on thesurface of the PEC and reflect it back to the magnetic field at thesense element. The result is a two-dimensional representation of thesensor footprint.

FIG. 10 shows the 2-D PEC model footprint for the sensor pictured inFIG. 25. FIG. 11 then shows the result when the footprint is convolvedwith a flaw representative of the one scanned in FIG. 4. The results arevery encouraging. The 2-D footprint model captures the double peak shapeof the response as well as the first peak being slightly larger than thesecond. The relative position of the two peaks is also accurate: thespacing between them is approximately 4.5″, which is the distancebetween the center of the two legs of the drive. Also, the larger of thetwo responses corresponds to when the drive leg that is closer to thesense element passes over the flaw for both the model and themeasurements. And finally, the footprint model accurately predicts thelarge blurring in the direction parallel to the drive.

There are two shortcomings of the 2-D PEC model. The first problem isthat the predicted size of the response is approximately 20% high—themodel predicts a maximal sensor response of 0.030″, when the sensorresponse is actually only 0.025″. This bias in predicted size holds forother flaw sizes as well.

The second shortcoming is more serious. The PEC footprint model providesonly a magnitude response (as there is no phase information from a PEC)and, therefore, expects all perturbations to behave similarly. Thisassumption is not valid. When looking at a near side flaw in steel, thethickness response and the lift-off response are not equivalent. Thethickness response seems to be centered around the location of the driveconductors while the lift-off response seems to be more centered aroundthe location of the sense element.

It is likely that this behavior is not captured because the PEC modelignores diffusion. A footprint model that relaxes the PEC requirement tocapture frequency dependent and material dependent diffusion effectswill be discussed in the Method CCC. This model will also be appropriatefor cylindrical coordinates.

Method CCC: Cylindrical Coordinate Footprint Model IncorporatingDiffusion Effects

In order to create a footprint model that takes into considerationfrequency and material properties and the associated diffusion effects,we need to determine a method for figuring out the current density inthe test object. When the test object is not a PEC, the method of imagecurrents is not available to us.

Method CCC accomplishes this with a clever application of the Love'sField Equivalence Principle [S. R. Rengarajan and Y. Rahmat-Samii, “TheField Equivalence Principle: Ilustration of the Establishment of theNon-Intuitive Null fields,” IEEE Antennas and Propagation Magazine, Vol.43, No. 4, August 2000]. The procedure for calculating the footprint isas follows:

Use an eddy current sensor model, potentially from Method XXX, todetermine the magnetic field everywhere in the presence of the testobject.

Use an eddy current sensor model model, potentially from Method XXX, todetermine the magnetic field everywhere in air (in the absence of a testobject).

Subtract the air response from the total response to use theSuperposition Principle, and determine the field everywhere due to theinduced eddy currents in the test object.

Use Love's Field Equivalence Principle, described by the geometry inFIG. 12, to represent the unknown induced eddy currents in the testobject as a surface current around free space.

Reflect that surface current back to the sense element to determine theimpedance response footprint of the sensor.

There are a few things to discuss about the assumptions of this model.First, while it does handle the layered media model, it onlyapproximates the footprint at the surface of the outermost layer of thetest object. For the case of CUI for example, one could argue that thisis not appropriate as the outermost layer is the weatherjacket. However,the presence of the weatherjacket only provides a phase shift at the lowfrequencies that are sensitive to the thickness of steel. Theweatherjacket does not change the relative sensitivity level. So,ignoring its presence for the case of the footprint analysis is not abad assumption.

Secondly, converting the footprint information into an expected flawresponse is more complicated than in the PEC model. In the PEC model,since only a magnitude footprint was calculated, this was convolved witha flaw response that was represented as a thickness change. Now, thefootprint convolution must be done in impedance space and then convertedback into properties of interest. This allows for a separate footprintfor each measured property.

The magnitude and phase footprint of the sensor pictured in FIG. 25 at10 Hz is shown in FIG. 13 for the flat plate configuration. The phasefootprint is very similar to the footprint calculated by the PEC model,as expected: the thickness response at 10 Hz is mostly in phase, and thePEC model was predictive of the sensor's thickness response. The phasefootprint is slightly wider than the PEC calcuated footprint causing thepredicted thickness response to the flaw scanned in FIG. 4 to drop from0.030″ predicted by the PEC model to 0.024″. Therefore, incorporatingdiffusion into the model eliminated the upward bias in predictedthickness response discussed in the Method BBB.

Furthermore, the magnitude of the footprint response is centered underthe sense element and only has a single peak. This corresponds to thelift-off response of the sensor, resolving the second shortcoming of the2-D PEC model discussed in Method BBB.

Sensor Design Optimization

The main motivation for developing the footprint models was to gainintuition as to how changes in the sensor geometry affected the sensor'ssensitivity to local defects. The desired ideal footprint would be a 2-Ddelta function: this would cause each measurement to be a perfect sampleof the material directly under the sensor.

The placement of the conductors allows for the manipulation of thefootprint perpendicular to the drive conductors. After trying manydifferent drive configurations, the design converged on a doublerectangular drive structure with the sense elements centered in one ofthe rectangles. The width of the rectangle was chosen to be 3.5″ inorder to achieve a similar sensitivity to steel thickness as the singlerectangular sensor used in previous measurements. FIG. 14 shows theimprovement of the sensor footprint. The main peak of the doublerectangular footprint is over twice as tall as the taller peak of thesingle rectangular footprint, which indicates improved sensitivity tolocal perturbations.

It should be noted that while a large, narrow peak for the sensorfootprint is desired, it should not be achieved at the cost of creatinga differential sensor. In other words, the integral of the sensorfootprint must not be close to zero. If this were the case, calibrationin air would be impossible.

The double rectangular sensor has other desirable characteristics.First, there is only one side lobe on either side of the main lobe, andthe lobes decay to zero quickly as compared to other designs. Anotherthing to notice is that the side lobes are anti-symmetric. That is,moving the sense elements into the other drive rectangle causes the sidelobes to flip. By creating a sense element that is the combination oftwo sense elements, one in either rectangle, we are left with an evenmore ideal footprint. This is shown in FIG. 15. The combined senseelement sensor has the advantage of the large peak without the largeside lobes.

The benefit of having the side lobes cancel is very significant. Inaddition to eliminating secondary peaks in the response as seen with thesingle rectangular sensor, the combined sense element sensor alsogreatly reduces unmodeled behavior. The model assumes that the testobject is a uniformly layered material: under this assumption the sidelobes would cancel. Using a single sense element requires material onone side of the sensor to cancel with material on the other side of thesensor. If the material is varying, this does not happen, and theproperty estimates would be corrupted by the unmodeled behavior.However, combining the two sense elements cancels out the side lobesusing the same material twice. Therefore, even if the material isvarying from one side of the sensor to the other, the measurements willmore closely adhere to the model.

FIG. 16 shows a flexible double row, double rectangular MR-MWM-Array.The drive is not visible because it was potted in an opaquepolyurethane. FIG. 17 shows the improvement in response when scanningthis sensor over the same 0.25″ flat plate with a 0.150″ deep, 3″diameter defect at 2″ of lift-off scanned in FIG. 4. The signal shape ismuch more representative and the response is 0.041″ as compared to theprevious response of 0.025″. The improvement provides the required SNRto detect the target 2 inch diameter, 0.050″ flaw.

The double-row sensor can be implemented without requiring twice as manychannels by placing the elements in series (in the case of a inductivesense element) or by using an adder stage (in the case of an activesense element like the MR element). Having the independent informationfrom both sensors, though, can provide information beyond simply addingthe two results together. So doubling the channel count may bebeneficial

In the case of an active element, such as the MR sensor, that issensitive to DC fields, the double row sensor has another large benefit.The two rows can be used to cancel unmodeled effects due to motionthrough a spatially varying DC fields. These spatially varying DC fieldscan be due to the Earth's magnetic field, perturbations of Earth'smagnetic field due to magnetic objects such as steel objects, and otherlocal magnetic fields. These unmodeled effects become more significantthe larger the spatial variation and the faster the sensor is movingthrough them.

Sensor Manufacture

Normal (absolute) and tangential (differential) fields have differentfootprint (SD)

FIG. 18 shows a method of constructing a sensor.

At step 1801, the winding fixture is set up based on the length andwidth of the drive. The width of the drive is determined by the desiredspatial wavelength of the sensor. The spatial wavelength is determinedbased on the intended application and may include such factors as thedesired sensor liftoff and the thickness of the materials under test.The drive length is determined by the length of the sense element array,the spatial wavelength, the expected liftoff, and the electromagneticproperties of the material under test.

At step 1803, the drive winding is wound using an insulated wire.Individual turns of the drive winding are placed together, either byhand or in a jig, such that the outer wires of each drive are in contactwith the wires of the adjacent turns. The wire may have an enamelcoating to provide electrical isolation between adjacent windings. Thecross section of the wire may be round, flat (i.e., rectangular), or anyother suitable cross section. In some embodiments, the drive winding iswound with each wire laterally adjacent to the next. The tension on thewire may be controlled to ensure that the winding doesn't lose tensionor otherwise deform. Control may be achieved by hand or using a using aspool tensioner. The tension on the wire may vary based on the sensorrequirements. The number of turns in the drive winding is controlled bythe sensor specification.

At step 1808, the wires are compressed to a pre-determined thickness sothat each drive has an identical winding thickness.

At step 1807, the drives are potted using a suitable potting compound.For example, a flexible urethane rubber. The mold has alignment featuresso that the drives can be accurately positioned later in the assemblyprocess. For example, posts can be added to the mold that produce holesin the rubber that can be placed onto alignment posts later in theassembly process. After the rubber has cured, the drive is removed andtrimmed. For sensors with multiple drive windings, multiple windings areproduced.

At step 1809 a thin bottom layer is applied to the bottom of the jig.This bottom layer can be pre-cut material or cast using a suitablepotting compound (such as urethane rubber). For urethane rubber, thelayer is allowed to partially cure. A partial cure allows subsequentlayers to fully adhere to the bottom layer while allowing the bottomlayer to have some stiffness.

At step 1811, a flexible PCB is placed on top of this bottom layer. ThePCB has alignment features (similar to the drive winding) that allow itto be aligned relative to the rest of the assembly. The drive winding orwindings are placed on top of the PCB using the same or other alignmentfeatures. The windings can be touching or separated by a fixed gap. Athin coating of urethane rubber is used between each layer to ensurethat they adhere to each other. Strain on the PCB is reduced by placingthe flexible PCB as close to the neutral bending plane of the sensor aspossible.

At step 1813 rubber is poured over the assembly and allowed to cure.

At step 1815 MR sensors and connectors are soldered to the PCB.

Section C: Instrument

The inventors have recognized and appreciated the need for impedanceinstrument 117 to provide high data rates, good signal-to-noise levels,wide bandwidth frequency operation (including low-frequenciesapproaching DC), and colocation in time and space of impedancemeasurements.

An embodiment of impedance analyzer 117 that achieves all of theseobjectives is presented with reference to FIG. 19A. Impedance analyzer117 includes signal generator 112, sensing hardware 114, and controlhardware 1910. Subcomponents of signal generator 112 may includereference signal generator 1901, combiner 1902, digital-to-analogconverter (DAC) 1903, signal conditioner 1904, and power amplifier 1905.Subcomponents of sense hardware 114 may include programmable gainamplifier 1906, anti-aliasing filter 1907, analog-to-digital converter(ADC) 1908 and multiply/accumulate block 1909.

Signal generator 1901, combiner 1902, multiply/accumulate block 1909,and control hardware 1910 are implemented in field-programmable gatearrays (FPGA). In one embodiment all subcomponents are implementedwithin the same FPGA, though multiple FPGAs may also be used. Amicroprocessor based implementation of the digital components is alsopossible, though currently impractical at the required data rates. Anembodiment of impedance analyzer 117 incorporates application-specificintegrated circuits (ASICs), i.e., custom integrated circuits to carryout the function of some or all components and subcomponents. It shouldbe appreciated that any suitable approach may be used.

The components and subcomponents of impedance analyzer 117 may bephysically located in a single “box” or separated in any suitable way.In some embodiments, the components are divided into an “Instrument” anda “Probe Electronics Unit” (PEU), as indicated in FIG. 19A. In otherembodiments all components are housed in a single common enclosure,reducing complexity, cost, and power consumption. Though it should beappreciated that other configurations may also be used. Some embodimentsuse a modular PEU design where a certain number of programmable gainamplifier 1906 are housed in a single unit and power amplifier 1905 ishoused separately. This allows the number of channels and drivessupported to be customized to a specific application by combiningvarying numbers of such PEU submodules.

Reference signal generator 1901 generates the signals, in digital form,that are used both to create excitation signal 121 ultimately applied tosensor 120 and as reference input to multiply/accumulate block 1909. Theoutputs of reference signal generator 1901 may include the in-phase andquadrature waveforms at one or more frequencies. The quadraturereference signal is a version of the in-phase reference signal shiftedone-quarter period (i.e., 90 degrees). The in-phase signals are providedto both combiner 1902 and multiply/accumulate block 1909; the quadraturesignals are provided to multiply/accumulate block 1909. These signalsare synchronized, which allows for the fully parallel measurement of thereal and imaginary components at all frequencies. Note that referencesignal generator 801 may also be used to create other waveforms, e.g.ramps, in addition to sinusoidal signals. Reference signal generator1901 may be implemented as a look-up table, i.e., where the output datais read from memory, as a real-time frequency generator that uses analgorithm to generate the data, or in any suitable way.

In some embodiments of reference signal generator 1909 all frequencygenerators may be clocked at the same clock frequency. The measurementfrequencies are chosen such that the clock frequency, f_(c), is an exactinteger multiple of the measurement frequency, f_(m). That isf_(c)=n×f_(m), where n is an integer. This results in all periods havingthe same number of samples per period, located at the same relative timepositions. This is critically important to the ability to take accuratemeasurements at high data rates, as it allows the multiply/accumulateblock 1909 to completely eliminate contamination from unwanted harmonicfrequencies using only a single half-period of data. Though, measurementfrequencies may also be used that are related to the clock frequency asintegral fractions, i.e., k×f_(c)=n×f_(m) where k and n are integers andk is a small number, in which case at least k periods would be neededper measurement. The number n may be chosen to be a power of 2 (2, 4, 8,16 . . . ) because this significantly simplifies the hardwareimplementation of block 809, transforming needed division operationsinto simple bit shift operations.

The accuracy (i.e., number of bits) of the digital representation of thesignals, both in the signal generator 112 and sensing hardware 114, ischosen such that the magnitude of the resulting quantization error issmaller than that of the minimum instrumentation noise due to the analogelectronics. Some example embodiments use 16-bit accuracy, though otherembodiments that use 14 bits have reduced power consumption with no lossof accuracy.

Combiner 1902 sums all the signals received from reference signalgenerator 1901. For example, combiner 1902 may combine signals ofdifferent frequencies. Combiner 1902 may apply different weights to thedifferent signals in the summation. Weights may be chosen to improve thesignal-to-noise ratios of the measurements at each frequency. If onlyone signal is provided by reference signal generator 1901, combiner 1902may simply act as a pass through, or may scale the signal. If multiplefrequencies are combined, an individual frequency's signal magnitude isless than what it would be if used alone, because the same outputmagnitude limit applies in both cases. Lower signal magnitude at aspecific frequency can result in lower signal-to-noise ratio. In suchcases it may be beneficial to carry out multiple frequenciessequentially. In some embodiments, combiner 802 may additionally applyphase shifts to the component signals.

The output signal of combiner 1902 is converted to analog form by DAC1903. Analog signals are represented by zig-zag lines in FIG. 19A, whiledigital signals are represented by simples lines.

The analog output of DAC 1903 is provided to drive signal conditioningmodule 1904. Module 1904 may include an anti-aliasing filter and aprogrammable attenuator stage.

The anti-aliasing filter is a low-pass filter that prevents aliasing byeliminating frequencies above one half of the sampling frequency. Insome embodiments, the filter features multiple-feedback active filterstages and passive RLC stages. Though, any suitable filter design may beused.

The programmable attenuator stage is necessary to provide the sensorwith the most appropriate drive level without reducing the magnitude ofthe DAC output, which would reduce accuracy. The programmableattenuation is controlled by the software. In one embodiment, theprogrammable attenuation stage is implemented as a sequence of multiplefixed-attenuation stages that may be selectively bypassed. In anotherimplementation variable gain is achieved by selecting from multiple tapsin a resistor divider ladder network. The multi-stage programmableattenuation architecture has significant advantages over traditionalvariable-gain amplifier (VGA) based implementations. These include muchlower thermal drift (gain changing with temperature) and noise.

The conditioned signal is provided from module 1904 to power amplifier1905 which uses it to generate excitation signal 121 applied to sensor120. Power amplifier 1905 supplies excitation signal 121 with sufficientcurrent as dictated by the sensor and application requirements. Whilesensor 120 is illustrated in this embodiment, it should be appreciatedthe any suitable device may be connected to impedance analyzer 117. Forexample, a device having two or more ports may be connected to impedanceanalyzer 117.

The impedance analyzer may have multiple signal generators 112,supplying excitation signals to more than one drive winding within thesame sensor or device, or to multiple sensors/devices. The separatesignal generators may operate at the same frequency or at differentfrequencies.

Sense hardware 114 receives response signal 123 from sensor 120. Whileonly one response signal 123 is shown in FIG. 19A, it should beappreciated that sensor 120 may have more than one sensor output. Insuch case, sense hardware 114 may be multiplexed, may be replicated suchthat sense hardware 114 contains multiple channel paths, each comprisedof blocks 1906, 1907, 1908, and 1909, or both multiplexing and parallelchannel paths may be used. The channel paths may be identical, but maybe adjusted for the respective response signal. For example,programmable-gain amplifier 1906 may have different setting in differentchannel paths.

Programmable-gain amplifier 1906 of sense hardware 114 receives responsesignal 123. Qualitatively, response signal 123 may be a very low-levelsignal—amplifier 1906 therefore provides amplification which allowsconversion to digital form with improved resolution and low noise. Theamplification factor (gain) is controlled by the software to select themost appropriate signal level to reach ADC 1908. Every channel can havea different gain setting. The highest signal-to-noise ratios areachieved when the signal magnitude at the input of the ADC is at thehighest possible level without exceeding the maximum input level.Though, a safety margin, 20% in one embodiment, is used to reduce therisk of accidentally exceeding the maximum ADC input level. Programmablegain amplifier 1906 may be implemented as a sequence of fixed-gainstages, with digitally controlled switches controlling whether eachstage is used or bypassed. The total gain of the programmable gainamplifier is the product of the gains of the individual non-bypassedstages. The individual stage gains are chosen such that an adequatelywide range of total gain values can be achieved, with an adequate numberof possible intermediate gain values. In one embodiment, the gains ofthe fixed-gain stages form a doubly-exponential sequence, e.g., g, g²,g⁴, g⁸, g¹⁶ . . . , resulting in possible gain values distributed evenlyon a logarithmic scale. The multi-stage programmable gain architecturehas significant advantages over traditional variable-gain amplifier(VGA) based implementations. These include much lower thermal drift(gain changing with temperature) and noise.

As noted above, in some embodiments, power amplifier 1905 andvariable-gain amplifier 1906 are located in a probe electronics unitwhich may be physically closer to sensor 120 than the remainingcomponents of impedance analyzer 117. Locating these components close tosensor 120 may improve signal-to-noise performance of impedance analyzer117.

Anti-aliasing filter 1907 is typical of any analog-to digital conversionsystem and is used to prevent undesired frequency componentscontributing to the final result. Its operation is very similar to theanti-aliasing filter in DSC 1904. Though, the two amplifiers may bedifferent, to accommodate their different positions in the signal chainand the different interface requirements of adjacent blocks. The analogsignal is converted to digital form by the ADC 1908.

Multiply/accumulate block 1909 carries out the digital multiplicationand low-pass filtering function analogous to those described withreference to FIG. 19B Block 1909 may include a separate parallelprocessing sub-block 1911-A for each component (real and imaginary) ofeach frequency. For example, in an embodiment that supports threefrequencies, there will be a total of six instances of block 1911 inblock 1909. Each block 1911 operates on the same input of digitalsamples from the ADC 1908. Each block 1911 uses a different referencesignal obtained from reference signal generator 1901. For example, theblock that computes the real component of the transimpedance atfrequency f₁ uses an in-phase sinusoidal reference signal with frequencyf₁, e.g., cos(2πf₁t), and the block that computes the imaginarycomponent of the transimpedance at frequency f₁ uses a quadrature (i.e.,shifted in phase by 90° sinusoidal reference signal with frequency f₁,e.g., sin(2πf₁t).

In typical legacy methods, all samples associated with a measurementmust be collected before any processing (e.g., Fast Fourier Transform)can be performed. In the embodiment of impedance analyzer 117 describedin connection with FIG. 19A, in each sub-block 1911 the data samplesreceived from ADC 1908 are processed according to method 1920, describedin connection with FIG. 19B. Advantageously, there is no requirement tobuffer multiple samples from ADC 1908 before processing by module 1909.At the beginning of a measurement, the cumulative sum value is set tozero in step 1921. At every clock cycle, a new sample is received fromADC 1908. In step 1922, this sample value is multiplied by thecorresponding reference signal value. After step 1922 is complete, thesample value is no longer needed and does not need to be saved. Theresult of the multiplication is added to the cumulative sum in step1923. Steps 1922 and 1923 are repeated for each incoming sample untilthe prescribed total number of samples per measurement have beenprocessed. The cumulative sum is divided by the total number of samplesper measurement in step 1925. The result of this division is the outputof method 1920, used by block 1911. The total number of samples permeasurement is chosen such that it is an exact integral multiple of thenumber of samples per period for each frequency. This results in theearlier stated requirement f_(c)=n×f_(m). As noted above, the totalnumber of samples per measurement is also chosen to be an exact power of2, which substantially simplifies and speeds up the division operationin step 1925 of method 1920 by transforming the division operation intoa simple bit shift operation.

As soon as method 1920 is complete and a measurement output value isobtained, method 1920 is executed again for the next measurement.

It is noted that all blocks 1911 operate in parallel on the same set ofinput samples. This process produces colocation in time and space of thereal and imaginary components of the impedance at all frequencies,overcoming limitations of existing impedance analyzers that produce thereal and imaginary parts of the impedance sequentially, inherentlyresulting in temporal differences and potentially resulting in spatialdifferences as well if, for example, the sensor is moving relative tothe test object. Having the real and imaginary parts of the impedance atall frequencies be generated from the data taken at the same location atthe same time may be used by algorithms, such as the multivariateinverse methods, which assume that the input quantities refer to thesame location and the same point in time.

In some embodiments, block 1909 is implemented as an FPGA, allowing forthe aforementioned parallel processing. Since these operations may beperformed in real time, only the obtained transimpedance data need to betransmitted out of the instrument (rather than exporting all datasamples). This allows for high data rates of, for example, 100, 1000s,or 10,000s of samples per second or more.

The control block 1910 configures and manages the operation of the otherblocks in impedance analyzer 117, based on instructions received frominstrument 110.

Section D: Detail of Data Processing

As discussed in connection with step 205 of method 200, impedance dataproduced by impedance analyzer 117 may be processed to produce estimateddata. Estimate data may represent electromagnetic properties, geometricproperties, material condition, or any type of measurement outcome. Likethe impedance data, the estimated data may be registered in time andspace.

FIG. 20 shows method 2000 for transforming “raw” impedance data obtainedfrom impedance analyzer 117 into the estimated data. As discussed inconnection with step 207, this output may be presented through userinterface 113 of instrument 110, or be passed to another apparatus forsubsequent action. Method 2000 may be viewed as an embodiment of step205 of method 200, though, method 2000 may be performed in isolation, oras part of any other suitable method.

At step 2001 raw impedance data is received and calibrated. Calibrationprocedures such as presented in [REFERENCE] may be used to convert theraw impedance data to “calibrated” impedance data. As discussed in REF,this step uses reference data obtained from on one or more knownmaterials, possibly including only air, to inform a data transformationprocedure. This procedure is tuned such that the transformedtransimpedance values of measurements on the reference material(s) matchthose generated for the precomputed database at step 201 of method 200,FIG. 2 (e.g., calculated by a model).

At step 2003, the calibrated impedance data produced by step 2001 may bepre-processed. As multivariate inverse methods can, under certaincircumstances, be very sensitive to instrumentation noise, i.e., signalvariations that are not correlated with physical properties of thematerial under test. Accordingly, in some embodiments, a digital filteris applied to the calibrated impedance data. For example, a low-passfilter in time and/or space may be applied to the calibrated impedancedata before it is converted to estimated data in subsequent steps. Anexample of such a filter is a weighted running average, with a weightingfunction such as a Gaussian “bell” curve or a “boxcar” function (equalweight given to all measurements in the window). Though, any suitablefilter may be used.

In some embodiments at step 2001 calibrated impedance data from two ormore channels is combined to produce a single impedance measurement.This step may be used, for example, to combine respective elements ofarrays 307 and 308 of sensor 300, (shown in FIG. 3D of US Publishedapplication 2013/0124109) to achieve a narrower sensor footprint.

The output of step 2003 is pre-processed data. In some applications,such as for detection of corrosion under insulation, commonly observedmaterial property variations (“material noise”) may be so large as tomask the signal (e.g., the property variation) of interest for theapplication. A recalibration procedure involving steps 2005 and 2007 maybe performed to improve visibility for such properties. In suchembodiments, a subset of the pre-processed data is designated as areference set. The reference set data may be taken from a location onthe test object where additional assumptions can be made about the testobject, further reducing the number of unknowns. This dataset may beobtained by acquiring data over sufficient area such that any defectshave only a negligible contribution.

At step 2005 the reference set of pre-processed data is converted by amultivariate inverse method (MIM) into estimated material propertiesusing the precomputed database generated at step 201 of method 200 andknown property assumptions for the nominal test object properties.Alternatively, the known property assumptions may be incorporated intothe database generation step, in which case that database will beutilized here at step 2005, while a second database that does notincorporate these assumptions is used at step 2009. The output of step2005 is re-calibration data.

At step 2007 a second calibration (re-calibration) is applied to thepre-processed data from step 2003. The re-calibration uses there-calibration data generated at step 2005. This step may be similar tostep 2001, however, here the reference data is the re-calibration dataobtained from test object itself rather than from a reference standard.As part of step 2007, but before the re-calibration data from the testobject is used for re-calibration, each of the reference materialproperties may be averaged across channels (using the same value foreach channel), or frequencies, or both. Using separate values for eachchannel makes it possible to account for actual channel-to-channelmaterial variation in the reference data set. The output of step 2007 isre-calibrated data.

At step 2009, the re-calibrated data is processed using the multivariateinverse methods and precomputed databases. In some embodiments thenumber of unknown properties is greater than at step 2005 since theassumption that the properties are nominal may no longer be applied. Theoutput of step 2009 is preliminary data.

At step 2011 the preliminary data is post processed to produce theestimated data. Similarly to step 2003, a digital filter or a runningaverage may be applied to the preliminary data. In contrast to thetreatment of instrument noise, which was addressed at step 2003,material noise, such as lift-off variation due to sensor motion orcomponent surface roughness, is addressed at step 2011, afterapplication of the multivariate inverse methods. The different treatmentof instrument noise and material noise is because material noiseassociated with one property will appear only in the estimates of onlythat property. Whereas attempting to filter the impedance data toaddress such variations in one property can lead to inaccurate estimatesin the other properties that are also part of the estimated data.

In some embodiments, at step 2011 a shape filter (reference needed) isapplied to the preliminary data. Shape filtering cross-correlates thepreliminary data with a “signature”, i.e., known spatial variation of anestimated property that results from the presence of a discrete flaw,such as a crack or inclusion. Shape filtering results in sharper (highermagnitude, lower width) indications. Signatures may be stored in alibrary and extracted, possibly via interpolation, based on known orestimated material properties.

In some embodiments, at step 2011 application-specific filtering used toselectively reject invalid data, e.g., property variations due tounmodeled physical effects. For example, such a filter is used to rejectCUI data in the vicinity of weather jacket straps, other pipes, physicalsupports, etc.

It should be appreciated that various embodiments of method 2000 may notinclude all steps presented here. For example, recalibration may not berequired for some applications; accordingly, step 2005 and 2007 may bebypassed and the method may proceed directly to step 2009. The requiredsteps may be determined by the specific application for which rawimpedance data is being processed. Other variations will be apparent toone of skill in the art.

Turning now to FIG. 21, an embodiment of instrument 110 is discussed.Instrument 110 may be used to perform method 200, and method 2000.Instrument 110 may be similar to instrument 110 as described inconnection with FIG. 1. Instrument 110 may include, for example, animpedance analyzer 117, processor 111, memory 115, user interface 113,network interface 119 and modules 109. Modules 109 may include acalibration module 2101, preprocessing module 2103, MIM module 2104,recalibration module 2105, post-processing module 2111, and assessmentmodule 2113.

Impedance analyzer 117 may be an analyzer such as described above inSection C. Impedance analyzer 117 may be used to collect raw impedancedata as described, for example, in connection with step 203.

Module 2101, is configured to implement step 2001 of method 2000.Specifically, calibration module 2101 calibrates raw impedance datareceived from impedance analyzer 117 using reference data 2117 which maybe stored in memory 115.

Preprocessing module 2103 is configured to implement step 2003 of method2000. Module 2103 receives calibrated impedance data provided bycalibration module Q1 and performs pre-processing as described above.Preprocessing module generates pre-processed data. A subset of thepre-processed data is designated as the reference set.

MIM module 2104 performs a multivariate inverse method to estimateproperties using pre-processed data provided by module 2103, aprecomputed database 2114, and, optionally, property assumptions 2115.Module 2104 may be used to perform steps 2005 and 2009 of method 2000.To assist in illustration of data flow within instrument 110, a stage 1block 2109 and stage 2 block 2107 are illustrated in module 2104. Block2109 receives the inputs associated with step 2005, while block 2107receives the inputs associated with step 2009. Specifically, as shown byblock 2109, MIM module 2104 may receive the reference set ofpre-processed data from preprocessing module 2103, database 2114, andproperty assumptions 2115 and perform a multivariate inverse method toprovide recalibration data in accordance with step 2005. As shown byblock 2107, MIM module 2104 may receive recalibrated data and database2114 to provide preliminary data in accordance with step 2001.

Recalibration module 2105, may be configured to receive recalibrationdata from MIM module 2104 (see block 2109) to recalibrate pre-processeddata. Recalibration module may be configured to implement step 2007 ofmethod 2000.

Post processing module 2111 may be configured to implement step 2011 ofmethod 2000. Module 2111 may be configured to receive preliminary datafrom MIM module 2104 and post-process the data to produce estimate data.The estimated data may be provided to assessment module 2113.

Assessment module 2113 may make an assessment of the estimate data.Module 2113 may be configured to perform step 207 of method 200, FIG. 2.

It should be appreciated that modules 109 of instrument 110 may includesuitable modules to perform methods 200 and 2000 in any suitable way toimplement.

3 Modeling of Eddy Current Sensors in Cylindrical Coordinates

The following sections describe a method for developing the precomputeddatabases of block 201 of FIG. 2. This is an extension into cylindricalcoordinates of the Cartesian coordinate forward model of the eddycurrent sensor found in [1]-[3] and based on the transfer relationsdeveloped by Professor Melcher [4]. The cylindrical coordinatederivation is necessary for accurately modeling the eddy current sensorinteraction when wrapped around a cylindrically shaped test object.Furthermore, since this model will be used in many applications wherethe material transport time interval determined by the characteristiclength of the eddy current sensor divided by the scanning speed iscomparable to the period of the sensor's current excitation, it will beimportant to incorporate the convective effect into the model [4].

The eddy current sensor is analyzed in the magnetoquasistatic (MQS)regime, which ignores the term due to displacement current in Ampere'slaw and assumes that the test object is comprised of very goodconductors and very good insulators This assumes that the spatial periodof the electromagnetic wave at the operating frequency is much greaterthan all other characteristic lengths including the spatial wavelengthof the winding construct. Therefore, the electrodynamic contribution isnegligible. Since the eddy current sensor is traditionally operatedbetween DC and 40 MHz, and the period of the winding construct isgenerally on the order of a few inches or smaller, this assumption isalways satisfied by at least 2-3 orders of magnitude. If the frequencyis raised much above 40 MHz, capacitive effects need to be considered[1, 4].

The eddy current sensor is also analyzed in the sinusoidal steady statewith angular frequency ω. Therefore, time dependent quantities canalways be written in the following form in the frequency domain:

$\begin{matrix}{{F( {\overset{\Gamma}{r},t} )} = {\; \{ {{\hat{F}( \overset{\Gamma}{r} )}e^{j\; \omega \; t}} \}}} & (3.1)\end{matrix}$

where {circumflex over (F)} is a complex amplitude function only ofspatial coordinates

. Therefore, derivatives in the time domain can be transformed intomultiplications by jω in the frequency domain.

The analysis of the eddy current sensor can be greatly simplified if thecurrent density in each drive winding can be considered uniform,although this is not necessary for the precomputed database generation.This assumption provides a known current density whose spatial Fouriermodes can be analyzed separately. The final magnetic field is simply thesuperposition of the individual solutions. The assumption is valid ifthe dimensions of the individual conductors are much smaller than theimposed spatial wavelength, the distance between the drive conductorsand the secondary conductors, and the distance between the sensorconductors and the test object. This is the case for the sensorsdeveloped for CUI (where in this document CUI includes both internal andexternal corrosion related wall loss for inspection from the outside ofa pipe, through insulation), for example. These models can be extendedinto the regime where these assumptions are invalid by using acollocation point method [1].

3.1 Motivation for the Cylindrical Eddy Current Sensor Model

Most standard eddy-current methods use a reference calibration methodwhen determining material properties or inspecting for flaws [Referenceand Air calibration, sometimes called standardization, are defined inreference 7-ASTM Std E-2338]. They use a set of known standards and thenempirically fit the resulting measurement to the known standard dataset.This often requires the assumption that properties other than the one ofinterest are constant. This is generally a terrible assumption—for thecase of CUI, variations in insulation thickness can be dramatic fromlocation to location and as described below the contribution of only a10% insulation thickness variation is huge compared to thre responsechange due to a 10% wall thickness change). Simply moving from the topof the pipe (or pipeline) to the bottom can result in insulation changeson the order of inches due to sagging caused by the weight of theinsulation itself.

FIG. 22 shows the relative impedance changes due to a 10% change in eachmaterial property for the CUI applications. All perturbations werearound a nominal 0.5″ thick steel plate with 2 inches of insulation, a0.02″ aluminum weatherjacket and a sensor lift-off of 0.5″. The data isnormalized so that the sensor response in air corresponds to 1+0j. It isclear from this plot that, unless there is good correction (bydeterministically removing the contribution from the response) for anyvariation in pipeline material properties, insulation thickness, andother relevant contributions, then small changes in thicknessmeasurement will get swamped out by the these variations. Unfortunately,the property of interest is the property to which the impedance measuredat the sensor terminals is the least sensitive—unless thesecontributions are deterministically removed. Since these materialproperty variations are inevitable, a reference calibration method isnot practical an the method ZZZ of calibrating in air and simultaneouslyestimating all properties using a multiple frequency inversion method isa justifiable approach. The goal is to enable the deterministic removalof the contributions of all major contributors to the impedance of thesensor, leaving only the wall thickness component. At the same time ifeach of these contributing elements, such as insulation thickness can bemeasured, their measurement provides a self-diagnostics capability sinceit is often known what there approximate values should be and what thereallowable ranges are. Thus, in one embodiment of this invention not onlyare their contributions removed from the total response to enablemeasurement of the wall thickness, but also each of them are measured tosupport self-diagnostics for the system and the procedure as it isperformed and in post inspection analysis.

As described in the following, the eddy current sensor models must beextended into cylindrical coordinates for applications such as CUI asthe Cartesian-coordinate assumption is not valid when wrapping an eddycurrent sensor around a pipe or pipeline. The air-point itself canchange by as much as 20% from a sensor being flat to being wrappedaround a pipe. Simply trying to normalize this effect out by using anair-point calibration at the correct diameter could result in as much asa 50% error in property measurement.

3.2 Eddy Current Sensor Forward Model in Cylindrical Coordinates: DriveAligned with Φ-Axis

This section contains the equations that predict the response of an eddycurrent sensor when wrapped around a cylindrical material in the typicalscan orientation preferred for the most applications. The model assumesthat the main legs of the primary winding are wrapped around thecylinder in the circumferential direction and that the periodicity ofthe primary winding is in the axial direction. Note that the periodicwinding construct is later relaxed so that aperiodic winding constructsare also modeled. Secondaries are assumed to be on either side of theprimary. Material properties are assumed to be independent of z, ϕ andtime. Material interfaces are assumed to be at cylindrical surfaces ofconstant ρ. FIG. 23 shows the modeled eddy current sensor structure.

3.2.1 Maxwell's Equations

In the MQS regime, magnetic fields H in the presence of conductingmaterials must satisfy the magnetic diffusion equation:

∇² H−jωσμH=0  (3.2)

When solving the magnetic diffusion equation, it is often easier toformulate the problem in terms of the magnetic vector potential A,defined as follows:

∇×A=B  (3.3)

Combining this definition with Faraday's law:

∇×E=−jωB  (3.4)

results in the following:

∇×E=∇×(−jωA)  (3.5)

This states that E and −jωA are vector fields with equal curl.Therefore, since vector fields with equal curl must be equal within anoffset of a gradient of a scalar field, we can formulate results in thefollowing:

E=(−jωA)−∇Φ  (3.6)

where Φ is known as the electric scalar potential. Next we take intoconsideration Ampere's law, neglecting the term due to displacementcurrent since we are in the MQS regime,

∇×H=J(3.7)

We also require Ohm's law, including the term due to the current inducedby the Lorentz force on the charge carriers, since the test object is inmotion.

J=σ(E+v×B)  (3.8)

Remembering B=μH we can perform the following calculations:

∇×μ⁻¹(∇×A)=−σ(jωA+∇Φ−v×B)  (3.9)

∇(∇·A)−∇² A=−jωμσA−∇(μσΦ)+μσ(v×∇×A)  (3.10)

∇² A−jωμσA=∇(∇·A+μσΦ)−μσ(ν×∇×A)  (3.11)

It is important to note that these steps implicity assume that alllayers of the test object are isotropic. That is, the off-diagonal termsof the conductivity and permeability tensor of each layer of the testobject are zero. This is a good assumption for most applications and formost metals, including steel and aluminum and the materials used forinsulating pipelines, satisfy this requirement.

Since Equation 3.3 only defined the magnetic vector potential withrespect to its curl, we have the freedom to define the magnetic vectorpotential's divergence in order to uniquely determine it within aconstant of integration. A convenient definition sets the first term ofthe RHS of Equation 3.11 to zero by letting

∇·A=−μσΦ  (3.12)

Therefore, we have reduced the problem to determining the magneticvector potential that satisfies

∇² A−jωμσA=−μσ(v×∇×A)  (3.13)

In the limit where v=0, Equation 3.13 further reduces to:

∇² A−jωμσA=0  (3.14)

Since the drive currents are only in the {circumflex over (ϕ)} directionand independent of ϕ as shown in FIG. 23, the magnetic vector potentialsolution to Equation 3.13 must also only have a {circumflex over (ϕ)}component and be independent of ϕ. Also, since all quantities areindependent of ϕ, the {circumflex over (ϕ)} component of the velocitycan be ignored, and we need only be concerned with the component (i.e.v=v_(z){circumflex over (z)}). So, Equation 3.13 reduces to:

$\begin{matrix}{{{\frac{1}{\rho}\frac{\partial}{\partial\rho}( {\rho \frac{\partial A_{\varphi}}{\partial\rho}} )} - \frac{A_{\varphi}}{\rho^{2}} + \frac{\partial^{2}A_{\varphi}}{\partial z^{2}} - {j\; \omega \; \mu \; \sigma \; A_{\varphi}} - {\mu \; \sigma \; v_{z}\frac{\partial A_{\varphi}}{\partial z}}} = 0} & (3.15)\end{matrix}$

It is important to note that when reducing Equation 3.13 to Equation3.15, taking the Laplacian of a vector in cylindrical coordinates is notas simple as applying the cylindrical coordinate Laplacian to eachcomponent of the vector. Making this mistake will result in adifferential equation with solution having an incorrect, non-physical pdependence based on a zeroth order Bessel function as opposed to thecorrect p dependence based on a first order Bessel function.

Using a separation of variables approach, we can postulate that A hasthe form

A=A _(ϕ) _(ρ) (ρ)A _(ϕ) _(z) (z){circumflex over (ϕ)}  (3.16)

and therefore Equation 3.15 further reduces to:

$\begin{matrix}{{{A_{\varphi_{z}}\lbrack {{\frac{1}{\rho}\frac{\partial}{\partial\rho}( {\rho \frac{\partial A_{\varphi_{\rho}}}{\partial\rho}} )} - \frac{A_{\varphi_{\rho}}}{\rho^{2}} - {j\; \omega \; \mu \; \sigma \; A_{\varphi_{\rho}}}} \rbrack} + {A_{\varphi_{\rho}}\lbrack {\frac{\partial A_{\varphi_{z}}}{\partial z^{2}} - {\mu \; \sigma \; v_{z}\frac{\partial A_{\varphi_{z}}}{\partial z}}} \rbrack}} = 0} & (3.17)\end{matrix}$

We choose for the z dependency of A_(ϕ) to have the following form withperiod λ:

$\begin{matrix}{{{A_{\varphi_{z_{n}}}(z)} = e^{{- {jk}_{n}}z}},{k_{n} = \frac{2\pi \; n}{\lambda}}} & (3.18)\end{matrix}$

The Fourier harmonic wavenumbers, k_(n), are used here as theperiodicity in the {circumflex over (z)} direction allows us torepresent the magnetic vector potential as the superposition of theFourier wavenumber modes, where n is any integer. Also, the sign of theexponent here is arbitrary since positive and negative complexwavenumbers need to be treated separately. This will be discussed laterin this section.

Plugging Equation 3.18 into Equation 3.17, we are left with thefollowing differential equation:

$\begin{matrix}{{e^{{- {jk}_{n}}z}\lbrack {\frac{\partial A_{\varphi_{\rho_{n}}}}{\partial\rho^{2}} + {\frac{1}{\rho}\frac{\partial A_{\varphi_{\rho_{n}}}}{\partial\rho}} + {( {{- k_{n}^{2}} - {j\; \mu \; {\sigma ( {\omega - {v_{z}k_{n}}} )}} - \frac{1}{\rho^{2}}} )A_{\varphi_{\rho_{n}}}}} \rbrack} = 0} & (3.19)\end{matrix}$

The above is a differential equation whose form is that of thetransformed version of the Bessel differential equation given by [5].

$\begin{matrix}{{\frac{d^{2}y}{{dx}^{2}} - {\frac{{2\; \alpha} - 1}{x}\frac{dy}{dx}} + {( {{\beta^{2}r^{2}x^{{2\; r} - 2}} + \frac{\alpha^{2} - {f^{2}r^{2}}}{x^{2}}} )y}} = 0} & (3.20)\end{matrix}$

whose solution is

y=x ^(α)[C ₁ J _(f)(βx ^(r))+C ₂ Y _(f)(βx ^(r))]  (3.21)

Equation 3.19 fits into this form where x=ρ, y=A_(ϕ) _(ρ) , α=0, r=1,f=1 and β=jγ_(n), and where the complex wavenumber γ_(n) is defined as

γ_(n)=√{square root over (k _(n) ² +jμσ(ω−ν_(z) k _(n)))}  (3.22)

Therefore, the solutions to Equation 3.19 are linear combinations ofJ₁(jγ_(n)ρ) and Y₁(jγ_(n)ρ), Bessel functions of the first and secondkind of the first order. Alternatively, the solution to Equation 3.19can be written in terms of linear combinations of I₁(γ_(n)ρ) andK₁(γ_(n)ρ), modified Bessel functions of the first and second kind ofthe first order. Therefore the full solution for each mode of themagnetic vector potential can be written as

$\begin{matrix}{A_{n} = {\lbrack {{a_{1}{I_{1}( {\gamma_{n}\rho} )}} + {a_{2}{K_{1}( {\gamma_{n}\rho} )}}} \rbrack e^{{- {jk}_{n}}z}\hat{\varphi}}} & (3.23)\end{matrix}$

It is interesting to note how velocity enters into the model. If amaterial is moving at velocity ν_(z) relative to a sensor, then theapparent frequency of excitation ω observed in that material is replacedby ω−νk_(n). This causes the presence of a non-zero velocity to breakthe symmetry around n=0 of the complex wavenumbers, requiring thatpositive and negative wavenumber modes be treated separately. This willbe discussed further in Section 2.2.

Before continuing, there are a few internal consistencies andassumptions that need to be explored. First of all, the solutions for Aprovided by Equation 3.23 have zero divergence. Therefore, revisitingthe gauge condition from Equation 3.12, the scalar potential Φ=0, andEquation 3.6 can be rewritten as

E=−jωA  (3.24)

Boundary conditions must be satisfied by Equation 3.24 in order for thismodel to be self consistent. First of all, at interfaces of conductingmaterials, where the tangential component of the electric field must becontinuous, the boundary condition is satisfied as A has {circumflexover (ϕ)} component which is tangential to the interface boundaries.However, this is not necessarily the case at the sensor windinginterface and in insulating regions near the sensor winding. Without an{circumflex over (r)} component to A and, therefore, E it appears thatelectric field continuity cannot be maintained. However, when theconductivity of a layer is zero, the electric scalar potential Φ is notforced to zero by Equation 3.12. So the inconsistency is resolved by anappropriate solution to ∇²Φ=0. Furthermore, the component of themagnetic field contributed by the non-zero electric scalar potential isdisregarded in the MQS regime. One important consequence of this is thatin order for the boundary condition at the winding surface to be met,the layers immediately adjacent to the winding must be insulating. Thiswas already necessary, however, in order to contain the winding currentswithin the winding.

Plugging Equation 3.23 into Equation 3.3 we can also make someobservations on the functional form of B.

$\begin{matrix}\begin{matrix}{B_{n} = {{\frac{\partial A_{\varphi_{n}}}{\partial z}\hat{\rho}} + {\frac{1}{\rho}\frac{\partial( {\rho \; A_{\varphi_{n}}} )}{\partial\rho}\hat{z}}}} \\{= {{{{jk}_{n}\lbrack {{a_{1}{I_{1}( {\gamma_{n}\rho} )}} + {a_{2}{K_{1}( {\gamma_{n}\rho} )}}} \rbrack}e^{{- {jk}_{n}}z}\hat{p}} +}} \\{{{\gamma_{n}\lbrack {{a_{1}{I_{1}( {\gamma_{n}\rho} )}} + {a_{2}{K_{0}( {\gamma_{n}\rho} )}}} \rbrack}e^{{- {jk}_{n}}z}\hat{z}}}\end{matrix} & (3.25)\end{matrix}$

At first glance it would appear that it is necessary to set a₂=0 inorder to prevent both components of both A and B from diverging as ρ→0.However, doing so would make it impossible to satisfy all of theboundary conditions presented by a layered-material problem. Thisapparent discrepancy is resolved by noting that the material layers arevarying in the {circumflex over (ρ)} direction and, therefore, only onelayer actually contains ρ=0. Only in that layer is it necessary fora₂=0. For numerical stability, it may be required to place a constrainton the minimum thickness of the layer surrounding ρ=0.

Furthermore, in order for the above MQS calculations to be valid, thematerials must either be good conductors with only a {circumflex over(ϕ)} component to E or good insulators with only a normal component toE. Another way of formulating this is to say that the magnetic diffusiontime, τ_(m)=μσl², must be much greater than the charge relaxation time,τ_(e)=ε/σ, for any test object with a non-zero conductivity. Theconductivities for which these two quantities become equal is determinedby the following equation:

$\begin{matrix}{\sigma = {\frac{1}{l}\sqrt{\frac{ɛ}{\mu}}}} & (3.26)\end{matrix}$

where l is a characteristic length scale such as the period of themagnetometer. Given the geometry of typical magnetometers, magneticdiffusion time is equal to charge relaxation time for conductivities onthe order of 0.1-1 S/m. Therefore, the MQS approximation is valid fortypical metals, which have conductivities in the mega-siemens per meterrange, or for good insulators with a conductivity on the order of 10⁻¹²S/m. For measurments on low conductivity materials, such as sea water,where the MQS approximation is not valid, the full set of Maxwell'sequations must be considered.

3.2.2 Symmetry Considerations

To simplify the computational complexity of the semi-analytical solutionto the eddy current sensor response, it is useful to exploit thesymmetry of the sensor geometry. If the origin of our coordinate systemis intelligently placed at the center of a primary winding as in FIG.23, we can make some useful observations.

First, if motion is neglected, we can note that the symmetry constrainsthe {circumflex over (ρ)}-component of the magnetic flux density to bean odd function of z, and it constrains the {circumflex over(z)}-component to be an even function of z. This forces the exponentialin the {circumflex over (ρ)} term to simplify to a sin(k_(n)z) and theexponential in the {circumflex over (z)} term to simplify to acos(k_(n)z). In terms of the magnetic vector potential A, this can beformalized as

$\begin{matrix}{{\frac{\partial A_{\varphi}}{\partial z}{_{z}{= {- \frac{\partial A_{\varphi}}{\partial z}}}}_{- z}},{A_{\varphi}{_{z}{= A_{\varphi}}}_{- z}}} & (3.27)\end{matrix}$

In order for this to be satisfied, according to Equation 3.23, A must bean even function of z. More specifically, its z dependence is governedby cos(k_(n)z). Therefore, in a series expansion of A, only non-negativewavenumber modes need be considered.

While this is convenient to use in the simplified, stationary case, thissymmetry breaks down in the presence of convection. When reflectedacross the ϕ−ρ plane, velocity in the {circumflex over (z)}-directionreverses and the even symmetry is broken. Therefore, in the presence ofconvection, positive and negative wavenumber modes must be consideredseparately.

The other symmetry to note is not broken by the presence of a non-zerovelocity: a half period shift in the {circumflex over (z)} directionreverses all currents, and, therefore, the sign of the magnetic vectorpotential. This can be formalized as

$\begin{matrix}{A_{\varphi}{_{z}{= {- A_{\varphi}}}}_{z + {\frac{1}{2}\lambda}}} & (3.28)\end{matrix}$

Since this translational symmetry condition cannot be satisfied by evenwavenumber modes, only odd wavenumber modes need be considered.

3.2.3 Fourier Series Expansion

The magnetic field (and, therefore, the magnetic vector potential) canbe represented as a superposition of all of the different Fourierwavenumber modes. Equation 3.23 provides the closed form solution foreach individual mode. Therefore, the magnetic vector potential can beexpressed as

$\begin{matrix}{{A_{\varphi}( {\rho,z} )} = {\sum\limits_{{n = {- \infty}},{odd}}^{\infty}\; {{A_{n}(\rho)}e^{{- {jk}_{n}}z}}}} & (3.29)\end{matrix}$

As mentioned in the previous section, only odd wavenumber modes arerequired due to the translational symmetry condition in Equation 3.28.

3.2.4 Sensor Interaction with Material: Normalized Surface ReluctanceDensity

Now that we have established a functional form for each wavenumber moden, it is necessary to establish how the test object interacts with theeddy current sensor. All of this information is contained within thenormalized surface inductance density, which is defined as:

$\begin{matrix}{{L_{n}( {\rho,z} )} = {k_{n}\frac{A_{\varphi_{n}}( {\rho,z} )}{H_{z_{n}}( {\rho,z} )}}} & (3.30)\end{matrix}$

In order to stay consistent with implementations of related models[1]-[3] we will use the inverse of the normalized surface inductancedensity, which has been referred to as the normalized surface reluctancedensity. Even though this is a slight misnomer (as the inverse ofreluctance is permeance, not inductance), there is no better term forthe inverse of inductance so it will be used in this document as well.The normalized surface reluctance density is defined as:

$\begin{matrix}{{R_{n}( {\rho,z} )} = {\frac{1}{L_{n}( {\rho,z} )} = {\frac{1}{k_{n}}\frac{H_{z_{n}}( {\rho,z} )}{A_{\varphi_{n}}( {\rho,z} )}}}} & (3.31)\end{matrix}$

Based on Equation 3.23, we can write

$\begin{matrix}{{{A_{\varphi}}_{n}( {\rho,z} )} = {{A_{n}(\rho)}e^{{- {jk}_{n}}z}}} & (3.32) \\{where} & \; \\{{A_{n}(\rho)} = {{a_{1}{I_{1}( {\gamma_{n}\rho} )}} + {a_{2}{K_{1}( {\gamma_{n}\rho} )}}}} & (3.33)\end{matrix}$

From Equation 3.25, we can write

$\begin{matrix}{{H_{z_{n}}( {\rho,z} )} = {{\frac{1}{\mu \; \rho}\frac{\partial( \; {\rho \; {A_{\varphi}}_{n}} )}{\partial\rho}} = {{H_{n}(\rho)}e^{{- {jk}_{n}}z}}}} & (3.34) \\{where} & \; \\{{H_{n}(\rho)} = {\frac{\gamma_{n}}{\mu}\lbrack {{a_{1}{I_{0}( {\gamma_{n}\rho} )}} - {a_{2}{K_{0}( {\gamma_{n}\rho} )}}} \rbrack}} & (3.35)\end{matrix}$

Therefore, plugging Equations 3.32 and 3.34 into Equation 3.31 we canconclude that

$\begin{matrix}{{R_{n}( {\rho,z} )} = {{R_{n}(\rho)} = {\frac{1}{k_{n}}\frac{H_{n}(\rho)}{A_{n}(\rho)}}}} & (3.36)\end{matrix}$

It is useful to first determine how R_(n)(ρ) behaves at the first andlast material interfaces, at ρ=ρ₀ and ρ=ρ_(N-1) respectively, as shownin FIG. 24. In the innermost material layer which contains ρ=0, it isnecessary for a₂=0, as K(γ_(n)ρ) diverges at ρ=0. Therefore, at theinnermost material interface

$\begin{matrix}{{R_{n}( \rho_{0} )} = {\frac{\gamma_{n}}{\mu \; k_{n}}\frac{I_{0}( {\gamma_{n}\rho_{0}} )}{I_{1}( {\gamma_{n}\rho_{0}} )}}} & (3.37)\end{matrix}$

In the outermost layer which contains ρ=∞, I(γ_(n)ρ) diverges as ρ→∞, sowe can immediately say that a₁=0. Therefore, at the outermost materialinterface

$\begin{matrix}{{R_{n}( \rho_{N - 1} )} = {{- \frac{\gamma_{n}}{\mu \; k_{n}}}\frac{K_{0}( {\gamma_{n}\rho_{0}} )}{K_{1}( {\gamma_{n}\rho_{0}} )}}} & (3.38)\end{matrix}$

One useful sanity check is that as ρ gets large, the cylindrical caseconverges to the Cartesian case, which is indeed the case [2].

$\begin{matrix}{{\lim\limits_{p->\infty}{R_{n}(\rho)}} = {{{- \frac{\gamma_{n}}{\mu \; k_{n}}}{\lim\limits_{p->\infty}\frac{K_{0}(\rho)}{K_{1}(\rho)}}} = {- \frac{\gamma_{n}}{\mu \; k_{n}}}}} & (3.39)\end{matrix}$

Given a transfer function that relates R_(n)(ρ_(i)) at one interface ofa layer of thickness t to the interface on the other side of the layerat R_(n)(ρ_(i+1))=R_(n)(ρ_(i)+t), it is possible to begin at theinnermost and outermost layer, apply the transfer function across eachlayer consecutively, and end up with an expression for the surfacereluctance density on either side of the plane of the sensor,R_(n)(ρ_(s) ⁺) and R_(n)(ρ_(s) ⁻). The difference between these twoquantities, defined as R_(n), can then be related back to the wavenumbermode of the surface current density in the plane of the windings, K_(s),as follows:

$\begin{matrix}{R_{n} = {{{R_{n}( \rho_{s}^{+} )} - {R_{n}( \rho_{s}^{-} )}} = {{\frac{1}{k_{n}}\frac{{H_{z_{n}}( {\rho_{s}^{+},z} )} - {H_{z_{n}}( {\rho_{s}^{-},z} )}}{{A_{\varphi}}_{n}( {\rho_{s},z} )}} = {\frac{1}{k_{n}}\frac{K_{S_{n}}}{A_{n}( \rho_{s} )}}}}} & (3.40) \\{\mspace{79mu} {where}} & \; \\{\mspace{79mu} {{K_{S}(z)} = {\sum\limits_{n = {- \infty}}^{\infty}\; {K_{S_{n}}e^{{- {jk}_{n}}z}}}}} & (3.41)\end{matrix}$

The desired transfer relation can be derived from Equation 25 in Section2.16 of [4] which formulates the magnetic vector potential everwhere ina layer in terms of its value at the two interfaces of the layer whichare at ρ=ρ_(i) and ρ=ρ_(i)+t:

$\begin{matrix}{{{{{A_{n}(\rho)} =}\quad}{A_{n}( \rho_{i} )}\frac{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} ){K_{1}( {\gamma_{n}\rho} )}} - {{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho} )}}}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{1}( {\gamma_{n}\rho_{i}} )}} - {{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}}} - {{A_{n}( {\rho + t} )}\frac{{I_{1}( {\gamma_{n}\rho_{i}} ){K_{1}( {\gamma_{n}\rho} )}} - {{K_{1}( {\gamma_{n}\rho_{i}} )}{I_{1}( {\gamma_{n}\rho} )}}}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{1}( {\gamma_{n}\rho_{i}} )}} - {{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}}}} & (3.42)\end{matrix}$

We can see that this equation must be true as both I₁ and K₁ satisfyEquation 3.19 and it is self-consistent at the two interfaces of thelayer. Using Equations 3.34, 3.36, and 3.42, we can formulate thefollowing equations for the surface reluctance density at the twointerface layers:

$\begin{matrix}{{R_{n}( \rho_{i} )} = {{{- \frac{\gamma_{n}}{\mu^{*}k_{n}}}\frac{\begin{matrix}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{\; 0}( {\gamma_{n}\rho_{i}} )}} +} \\{{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{0}( {\gamma_{n}\rho_{i}} )}}\end{matrix}}{\begin{matrix}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{\; 1}( {\gamma_{n}\rho_{i}} )}} -} \\{{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}\end{matrix}}} + {\frac{\gamma_{n}}{\mu^{*}k_{n}}\frac{\begin{matrix}{{{I_{1}( {\gamma_{n}\rho_{i}} )}{K_{\; 0}( {\gamma_{n}\rho_{i}} )}} +} \\{{K_{1}( {\gamma_{n}\rho_{i}} )}{I_{0}( {\gamma_{n}\rho_{i}} )}}\end{matrix}}{\begin{matrix}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{\; 1}( {\gamma_{n}\rho_{i}} )}} -} \\{{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}\end{matrix}}\frac{A_{n}( {\rho + t} )}{A_{n}( \rho_{i} )}}}} & (3.43) \\{{R_{n}( {\rho_{i} + t} )} = {{{- \frac{\gamma_{n}}{\mu^{*}k_{n}}}\frac{\begin{matrix}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{\; 0}( {\gamma_{n}( {\rho_{i} + t} )} )}} +} \\{{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{0}( {\gamma_{n}( {\rho_{i} + t} )} )}}\end{matrix}}{\begin{matrix}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{\; 1}( {\gamma_{n}\rho_{i}} )}} -} \\{{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}\end{matrix}}\frac{A_{n}( \rho_{i} )}{A_{n}( {\rho_{i} + t} )}} + {\frac{\gamma_{n}}{\mu^{*}k_{n}}\frac{\begin{matrix}{{{I_{1}( {\gamma_{n}\rho_{i}} )}{K_{\; 0}( {\gamma_{n}( {\rho_{i} + t} )} )}} +} \\{{K_{1}( {\gamma_{n}\rho_{i}} )}{I_{0}( {\gamma_{n}( {\rho_{i} + t} )} )}}\end{matrix}}{\begin{matrix}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{\; 1}( {\gamma_{n}\rho_{i}} )}} -} \\{{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}\end{matrix}}}}} & (3.44)\end{matrix}$

Finally, we can combine Equations 3.43 and 3.44, eliminating A_(n) fromthe expression, leaving us with a transfer function that relates thesurface reluctance density at one layer interface to the next.

$\begin{matrix}{\mspace{79mu} {{R_{n}( {\rho_{i} + t} )} = {{G_{n}( {\rho_{i} + t} )} + {{F_{n}( {\rho_{i} + t} )}\frac{G_{n}( \rho_{i} )}{{R_{n}( \rho_{i} )} - {F_{n}( \rho_{i} )}}}}}} & (3.45) \\{\mspace{79mu} {where}} & \; \\{{F_{n}(x)} = {{- \frac{\gamma_{n}}{\mu^{*}k_{n}}}\frac{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{0}( {\gamma_{n}x} )}} + {{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{0}( {\gamma_{n}x} )}}}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{1}( {\gamma_{n}\rho_{i}} )}} - {{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}}}} & (3.46) \\{{G_{n}(x)} = {{+ \frac{\gamma_{n}}{\mu^{*}k_{n}}}\frac{{{I_{1}( {\gamma_{n}\rho_{i}} )}{K_{0}( {\gamma_{n}x} )}} + {{K_{1}( {\gamma_{n}\rho_{i}} )}{I_{0}( {\gamma_{n}x} )}}}{{{I_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{K_{1}( {\gamma_{n}\rho_{i}} )}} - {{K_{1}( {\gamma_{n}( {\rho_{i} + t} )} )}{I_{1}( {\gamma_{n}\rho_{i}} )}}}}} & (3.47)\end{matrix}$

3.2.5 Implementation and Validation

Since the current densities in the plane of the primary windings can beconsidered uniform for this model, as discussed earlier, the magneticfield at the sense element due to a unit current excitation in thepresence of the test object can be determined using the following steps:

1. Define the current density in the primary windings based on knowledgeof the sensor geometry and winding position and using the uniformcurrent density assumption. Take the Fourier transform of the currentdensity profile to determine the wavenumber modes of the surface currentdensity.

2. For each wavenumber mode, start at the innermost and outermostmaterial interface and apply the transfer functions defined in Section2.4 to determine the surface reluctance density on either side of theplane of the primary windings.

3. Calculate the magnetic vector potential in the plane of the primarywindings for each wavenumber mode using Equation 3.40. Convert this tothe magnetic vector potential in the plane of the sense element usingEquation 3.42.

4. Calculate the magnetic field for each wavenumber mode at the senseelement using Equation 3.25.

5. Determine the total magnetic field at the sense element due to a unitcurrent excitation by summing the individual wavenumber modes.

While the above steps are relatively simple to implement in Matlab orother such software packages, care must be taken to make the simulationefficient. The two most important parameters that can be adjusted toaffect the trade-off between simulation time and simulation accuracy arethe simulation extent and the sampling interval. Based on the size ofthe sensor, a simulation extent needs to be chosen such that the modelassumption that the sensor is infinitely periodic, when the sensor isactually finite, does not degrade the simulation accuracy. Furthermore,a sampling interval must be chosen that is small enough so that thedrive excitation can be accurately represented, and so that high enoughwavenumber modes can be calculated. As expected, as the samplinginterval decreases, or as the simulation extent increases for a givensampling interval, the simulation time increases. In practice,simulation convergence is accomplished when the simulation extent is5-10 times the size of the sensor. For the sensor geometries used forthe CUI application, a sampling interval of 1 mm is necessary.

Furthermore, Bessel functions are expensive (in terms of time) tocalculate in Matlab. Much simulation time can be saved by taking intoconsideration the assymptotic nature of the modified Bessel function astheir argument gets large [6]. It is interesting to note that this isthe equivalent of using the Cartesian coordinate model for large ρ.

One of the main difficulties in validating the derived model wasmanufacturing an appropriate sensor. Many iterations were requiredbefore a sensor construct was created satisfying the requirements of themodel. Thus, one embodiment of this invention is the iterative design ofa sensor that has a response that matches the model predicted response,by empirically comparing the sensor and model responses and modifyingthe design to obtain close agreement using intuition gained from themodels and empirical data. The two most difficult requirements werecreating a many-turn drive winding where the location of each windingwas accurately known and maintaining the sense element's positionrelative to the winding when the sensor is wrapped around a cylinder.FIG. 25 shows the first sensor that successfully matched the models. Aflat wire with a 2:1 aspect ratio was used for the drive winding sothat, when constructing a multiple turn winding, the position of eachwire could be more easily controlled because each wire lies verticallynext to the last. Other such desgins that maintain the sensor windingpositional integrity are also included in this invention. The flexibleprinted circuit board with the MR elements is potted with the drivewinding such that the elements are on the same bending axis as the drivewire. Therefore, regardless of the radius of curvature, the MR elementsare in the same cylindrical surface as the drive.

FIG. 26 and FIG. 27 show the results that validated the cylindricalmodel implementation. FIG. 26 shows that the model successfully predictsthe air responses of the sensor when wrapped around plastic cylinders ofvarying diameters. The response of the sensor in air when flat wasnormalized to 1+0j. Only the magnitude of the impedance response isplotted as the phase was always zero. The RMS error of the measured airresponses as compared to the model-predicted air responses is under0.05%. This is well within the tolerances of the experimental setup.FIG. 27 shows the results of taking measurements on a 6.625″ diameter,0.25″ wall thickness pipe at varying lift-offs plotted on alift-off/thickness grid. The air point represents the sensor's responsein air when at a diameter of 10.625″ (6.625″ pipe+2″ of insulation). Asthe lift-off is increased, the data follows the lift-off line up towardsthe air point. As the lift-off increased from 0.5″ to 2.5″, theestimated thickness varied only by ±0.002″, with estimates ranging from0.248″ to 0.251″. Lift-off lines are defined as lines in the visualrepresentation of the precomputed database for which only the lift-offvaries and other properties are constant.

3.3 Eddy Current Sensor Forward Model in Cylindrical Coordinates: DriveAligned with Z-Axis

Depending on the specifics of an application, it may be necessary toscan a pipe or pipeline circumferentially, with the drive aligned alongthe pipeline's axis. This section contains the equations that predictthe response of an eddy current sensor when wrapped around a pipe inthis orientation. The model assumes that the main legs of the primarywinding are aligned with the axis of the pipe and that the periodicityof the primary winding is in the circumferential direction. Secondariesare assumed to be on either side of the primary. Material properties arestill assumed to be independent of z, ϕ and time and material interfacesare still assumed to be at cylindrical surfaces of constant ρ. FIG. 28shows the modeled eddy current sensor structure.

3.3.1 Maxwell's Equations

In this formulation, we can begin with Equation 3.13. Assuming that thesensor is periodic in the {circumflex over (ϕ)} direction with period λand that the drive currents are only in the {circumflex over (z)}direction and independent of z as shown in FIG. 28, the magnetic vectorpotential solution to Equation 3.13 must also only have a {circumflexover (z)} component and be independent of z. Also, since all quantitiesare independent of z, the {circumflex over (z)} component of thevelocity can be ignored, and we need only be concerned with the{circumflex over (ϕ)} component (i.e. v=ν_(ϕ){circumflex over (ϕ)}).Furthermore, during scanning, the material moves with a common angularvelocity (i.e. v=ρω_(ϕ){circumflex over (ϕ)}). So, Equation 3.13 reducesto:

$\begin{matrix}{{{\frac{1}{\rho}\frac{\partial}{\partial\rho}( {\rho \frac{\partial A_{z}}{\partial\rho}} )} + {\frac{1}{\rho^{2}}\frac{\partial^{2}A_{z}}{\partial\varphi^{2}}} - {j\; {\omega\mu}\; \sigma \; A_{z}} - {{\mu\sigma\omega}_{\varphi}\frac{\partial A_{z}}{\partial\varphi}}} = 0} & (3.48)\end{matrix}$

For this geometry, it is important to note that the angular periodicityin the {circumflex over (ϕ)} direction must be limited to integerdivisors of 2π. That is,

${\lambda = {{\frac{2\pi}{n}\rho \mspace{14mu} {where}\mspace{14mu} n} = 1}},2,{3\mspace{11mu} \ldots}$

We can use a separation of variables approach and postulate that A hasthe form

A=A _(z) _(ρ) (ρ)A _(z) _(ϕ) (ϕ){circumflex over (z)}  (3.49)

and therefore Equation 3.48 further reduces to

$\begin{matrix}{{{A_{z_{\varphi}}\lbrack {{\frac{1}{\rho}\frac{\partial}{\partial\rho}( {\rho \frac{\partial A_{z_{\rho}}}{\partial\rho}} )} - {j\; {\omega\mu}\; \sigma \; A_{z_{\rho}}}} \rbrack} + {A_{z_{\rho}}\lbrack {{\frac{1}{\rho^{2}}\frac{\partial^{2}A_{z_{\varphi}}}{\partial\varphi^{2}}} - {\mu \; {\sigma\omega}_{\varphi}} + \frac{\partial^{2}A_{z_{\varphi}}}{\partial\varphi}} \rbrack}} = 0} & (3.50)\end{matrix}$

Knowing the structure of the sensor's periodicity in the {circumflexover (ϕ)}-direction, we can say that the ϕ dependency of A_(z) has theform

$\begin{matrix}{{A_{z_{\varphi_{n}}}(\varphi)} = e^{{- {jn}}\mspace{11mu} \varphi}} & (3.51)\end{matrix}$

Similarly to the previous derivation, the sign of the exponent here isarbitrary since positive and negative complex modes need to be treatedseparately because of the lack of symmetry due to the velocity term.

Plugging Equation 3.51 into Equation 3.50, we are left with thefollowing differential equation:

$\begin{matrix}{{e^{{- {jn}}\mspace{11mu} \varphi}\lbrack {\frac{\partial^{2}A_{z_{\rho_{n}}}}{\partial\rho^{2}} + {\frac{1}{\rho}\frac{\partial A_{z_{\rho_{n}}}}{\partial\rho}} + {( {\frac{- n^{2}}{\rho^{2}} - {j\; \mu \; {\sigma ( {\omega - {\omega_{\varphi}n}} )}}} )A_{z_{\rho_{n}}}}} \rbrack} = 0} & (3.52)\end{matrix}$

Equation 3.52 is in the familiar form of the tranformed Bessel functionequation where x=ρ, y=A_(z) _(ρ) , α=0, r=1, f=n and β=jγ_(n′), where wedefine the complex wavenumber, γ_(n′), as

γ_(n′)=√{square root over (jμσ(ω−ω_(ϕ) n))}  (3.53)

Therefore, the full solution for the magnetic vector potential for thegeneral case, with drive wires aligned axially, can be written as

A _(n)=[a ₁ I _(n)(γ_(n′)ρ)+a ₂ K _(n)(γ_(n′)ρ)]e ^(−jnϕ) {circumflexover (z)}  (3.54)

The case where σ=0 must be considered separately as the arguments of thebessel functions would be equal to zero. In this case the solution tothe magnetic vector potential is much simpler

A _(n) =└a ₁ρ^(n) +a ₂ρ^(−n) ┘e ^(−jnϕ) {circumflex over (z)}  (3.55)

The angular velocity enters into this model in a similar manner asbefore. If a material is moving at angular velocity ω_(ϕ) relative to asensor, then the apparent frequency of excitation ω observed in thatmaterial is replaced by ω−ω_(ϕ)n. This again causes non-zero velocity tobreak the symmetry around n=0 of the wavemodes, requiring that positiveand negative wavemodes be treated separately. This will be discussedfurther in the next section.

Plugging Equation 3.54 into Equation 3.3 provides us with a formulationfor B.

$\begin{matrix}\begin{matrix}{B_{n} = {{\frac{1}{\rho}\frac{\partial A_{z_{n}}}{\partial\varphi}\hat{\rho}} - {\frac{\partial A_{z_{n}}}{\partial\rho}\hat{\varphi}}}} \\{= {{{- {\frac{jn}{\rho}\lbrack {{a_{1}{I_{n}( {\gamma_{n^{\prime}}\rho} )}} + {a_{2}{K_{n}( {\gamma_{n^{\prime}}\rho} )}}} \rbrack}}e^{{- {jn}}\mspace{11mu} \varphi}\hat{\rho}} -}} \\{{{\gamma_{n^{\prime}}\lbrack {{a_{1}{I_{n}^{\prime}( {\gamma_{n^{\prime}}\rho} )}} - {a_{2}{K_{n}^{\prime}( {\gamma_{n^{\prime}}\rho} )}}} \rbrack}e^{{- {jn}}\mspace{11mu} \varphi}\hat{\varphi}}}\end{matrix} & (3.56) \\{where} & \; \\{{{K_{n}^{\prime}( {\gamma_{n^{\prime}}\rho} )} = \frac{{K_{n - 1}( {\gamma_{n^{\prime}}\rho} )} + {K_{n + 1}( {\gamma_{n^{\prime}}\rho} )}}{2}},{{I_{n}^{\prime}( {\gamma_{n^{\prime}}\rho} )} = \frac{{I_{n - 1}( {\gamma_{n^{\prime}}\rho} )} + {I_{n + 1}( {\gamma_{n^{\prime}}\rho} )}}{2}}} & (3.57)\end{matrix}$

It is necessary to set a₂=0 in the material layer that contains ρ=0 inorder to prevent both components of both A and B from diverging as ρ→0.For numerical stability, it may be required to place a constraint on theminimum thickness of the layer surrounding ρ=0. For the case where σ=0,Equation 3.56 leads to

$\begin{matrix}{B_{n} = {{{\frac{- {jn}}{\rho}\lbrack {{a_{1}\rho^{n}} + {a_{2}\rho^{- n}}} \rbrack}e^{{- {jn}}\mspace{11mu} \varphi}\hat{z}} - {{\frac{n}{\rho}\lbrack {{a_{1}\rho^{n}} + {a_{2}\rho^{- n}}} \rbrack}e^{{- {jn}}\mspace{11mu} \varphi}\hat{\varphi}}}} & (3.58)\end{matrix}$

3.3.2 Symmetry Considerations

The symmetry conditions in this model that persist in the presence ofconvection are analagous to the previous model. A half-period shift inthe {circumflex over (ϕ)} direction reverses all currents, and,therefore, the sign of the magnetic vector potential. This can beformalized as

A _(z)|_(ϕ) =−A _(z)|_(ϕ+π)  (3.59)

Since this rotational symmetry condition cannot be satisfied by evenwavenumber modes, only odd wavenumber modes need be considered.

3.3.3 Fourier Series Expansion

The periodicity of the sensor in the {circumflex over (ϕ)} directionallows us to represent the magnetic field and the magnetic vectorpotential as a superposition of the different wavemodes. Equation 3.54provides the closed form solution for each individual mode. The magneticvector potential can be expressed as

$\begin{matrix}{{A_{z}( {\rho,\varphi} )} = {\sum\limits_{{n = {- \infty}},{odd}}^{\infty}\; {{A_{n}(\rho)}e^{{- {jn}}\mspace{11mu} \varphi}}}} & (3.60)\end{matrix}$

As mentioned in the previous section, only odd wavenumber modes arerequired due to the translational symmetry condition in Equation 3.59.

3.3.4 Sensor Interaction with Material: Normalized Surface ReluctanceDensity

The test object's interaction with the eddy current sensor ischaracterized by the surface reluctance density, now defined as

$\begin{matrix}{{R_{n}( {\rho,\varphi} )} = {\frac{1}{L_{n}( {\rho,\varphi} )} = {{\frac{1}{k_{n}}\frac{H_{\varphi_{n}}( {\rho,\varphi} )}{A_{z_{n}}( {\rho,\varphi} )}} = {\frac{\rho}{n}\frac{H_{\varphi_{n}}( {\rho,\varphi} )}{A_{z_{n}}( {\rho,\varphi} )}}}}} & (3.61)\end{matrix}$

Our formulation follows the same logic as in the previous model. Basedon Equation 3.54, we can write

A _(z) _(n) (ρ,ϕ)=A _(n)(ρ)e ^(−jnϕ)  (3.62)

where

A _(n)(ρ)=a ₁ I _(n)(γ_(n′)ρ)+a ₂ K _(n)(γ_(n′)ρ)  (3.63)

or when σ=0,

A _(n)(ρ)=a ₁ρ^(n) +a ₂ρ^(−n)  (3.64)

From Equation 3.56, we can write

$\begin{matrix}{{H_{\varphi_{n}}( {\rho,\varphi} )} = {{{- \frac{1}{\mu}}\frac{\partial A_{z}}{\partial\rho}} = {{H_{n}(\rho)}e^{{- {jn}}\mspace{11mu} \varphi}}}} & (3.65) \\{where} & \; \\{{H_{n}(\rho)} = {- {\frac{\gamma_{n^{\prime}}}{\mu}\lbrack {{a_{1}{I_{n^{\prime}}( {\gamma_{n^{\prime}}\rho} )}} - {a_{2}{K_{n}^{\prime}( {\gamma_{n^{\prime}}\rho} )}}} \rbrack}}} & (3.66)\end{matrix}$

or when σ=0,

$\begin{matrix}{{H_{n}(\rho)} = {- {\frac{n}{\rho}\lbrack {{a_{1}\rho^{n}} - {a_{2}\rho^{- n}}} \rbrack}}} & (3.67)\end{matrix}$

Therefore, plugging Equations 3.62 and 3.65 into Equation 3.61 we canconclude that

$\begin{matrix}{{R_{n}( {\rho,\varphi} )} = {{R_{n}(\rho)} = {\frac{\rho}{n}\frac{H_{n}(\rho)}{A_{n}(\rho)}}}} & (3.68)\end{matrix}$

It is useful to first determine how R_(n)(ρ) behaves at the first andlast material interfaces, at ρ=ρ₀ and ρ=ρ_(N-1) respectively, as shownin FIG. 24. In the innermost material layer which contains ρ=0, it isnecessary for a₂=0, as K diverges at ρ=0. Therefore, at the innermostmaterial interface

$\begin{matrix}{{R_{n}( \rho_{0} )} = {{- \frac{{\rho\gamma}_{n^{\prime}}}{\mu \; n}}\frac{I_{n}^{\prime}( {\gamma_{n^{\prime}}\rho_{0}} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{0}} )}}} & (3.69)\end{matrix}$

or when σ=0, simply

$\begin{matrix}{{R_{n}( \rho_{0} )} = {- \frac{1}{\mu}}} & (3.70)\end{matrix}$

Note that in this case, R_(n) has the opposite sign as compared to theanalagous Cartesian and circumferential-drive cylindrical cases. This isbecause when the roles of ρ and ϕ in the coordinate system are swapped,the right-hand rule requires that the normal component of the magneticflux points in the opposite direction.

In the outermost layer which contains ρ=∞, I diverges as ρ→∞, so we canimmediately say that a₁=0. Therefore, at the outermost materialinterface

$\begin{matrix}{{R_{n}( \rho_{N - 1} )} = {\frac{\rho \; \gamma_{n^{\prime}}}{\mu \; n}\frac{K_{n}^{\prime}( {\gamma_{n^{\prime}}\rho_{0}} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{0}} )}}} & (3.71)\end{matrix}$

or when σ=0, simply

$\begin{matrix}{{R_{n}( \rho_{N - 1} )} = \frac{1}{\mu}} & (3.72)\end{matrix}$

Once again we want a transfer function that relates R_(n)(ρ_(i)) at oneinterface of a layer of thickness t to the interface on the other sideof the layer at R_(n)(ρ_(i+1))=R_(n)(ρ_(i)+t). This would make itpossible to begin at the innermost and outermost layer, apply thetransfer function across each layer consecutively, and end up with anexpression for the surface reluctance density on either side of theplane of the sensor, R_(n) (ρ_(s) ⁺) and R_(n)(ρ_(s) ⁻). The differencebetween these two quantities, defined as R_(n), can then be related backto the wavenumber mode of the surface current density in the plane ofthe windings, K_(S), as follows:

$\begin{matrix}{R_{n} = {{{R_{n}( \rho_{s}^{+} )} - {R_{n}( \rho_{s}^{-} )}} = {{\frac{\rho}{n}\frac{{H_{\varphi_{n}}( {\rho_{s}^{+},\varphi} )} - {H_{\varphi_{n}}( {\rho_{s}^{-},\varphi} )}}{A_{z_{n}}( {\rho_{s},\varphi} )}} = {\frac{\rho}{n}\frac{K_{S_{n}}}{A_{n}( \rho_{s} )}}}}} & (3.73) \\{\mspace{79mu} {where}} & \; \\{\mspace{79mu} {{K_{S}(\varphi)} = {\sum\limits_{n = {- \infty}}^{\infty}{K_{S_{n}}e^{{- {jn}}\; \varphi}}}}} & (3.74)\end{matrix}$

This transfer relation can be derived from the analagous equation toEquation 25 in Section 2.16 of [4] which formulates the magnetic vectorpotential everwhere in a layer in terms of its value at the twointerfaces of the layer which are at ρ=ρ_(i) and ρ=ρ_(i)+t:

$\begin{matrix}{{A_{n}(\rho)} = {{{A_{n}( \rho_{i} )}\mspace{11mu} \frac{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}} - {{A_{n}( {\rho_{i} + t} )}\mspace{11mu} \frac{{{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{K_{n}( {\gamma_{n^{\prime}}\rho} )}} - {{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{I_{n}( {\gamma_{n^{\prime}}\rho} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}}}} & (3.75)\end{matrix}$

We can see that this equation must be true as both I_(n)(γ_(n′)ρ) andK_(n)(γ_(n′)ρ) satisfy Equation 3.52 and it is self-consistent at thetwo interfaces of the layer. Using Equations 3.65, 3.68, and 3.75, wecan formulate the following equations for the surface inductance densityat the two interface layers:

$\begin{matrix}{{R_{n}( \rho_{i} )} = {{\frac{\rho \; \gamma_{n^{\prime}}}{\mu \; n}\frac{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}^{\prime}( {\gamma_{n^{\prime}}\rho_{i}} )}} + {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}^{\prime}( {\gamma_{n^{\prime}}\rho_{i}} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}} - {\frac{\rho \; \gamma_{n^{\prime}}}{\mu \; n}\frac{{{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{K_{n}^{\prime}( {\gamma_{n^{\prime}}\rho_{i}} )}} + {{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{I_{n}^{\prime}( {\gamma_{n^{\prime}}\rho_{i}} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}\frac{A_{n}( {\rho_{i} + t} )}{A_{n}( \rho_{i} )}}}} & (3.76) \\{{R_{n}( {\rho_{i} + t} )} = {{\frac{\rho \; \gamma_{n^{\prime}}}{\mu \; n}\frac{\begin{matrix}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}^{\prime}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}} +} \\{{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}^{\prime}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}}\end{matrix}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}\frac{A_{n}( \rho_{i} )}{A_{n}( {\rho_{i} + t} )}} - {\frac{\rho \; \gamma_{n^{\prime}}}{\mu \; n}\frac{{{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{K_{n}^{\prime}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}} + {{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{I_{n}^{\prime}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}}}} & (3.77)\end{matrix}$

Finally, we can combine Equations 3.76 and 3.77, eliminating A_(n) fromthe expression, leaving us with a transfer function that relates thesurface reluctance density at one layer's interface to the next.

$\begin{matrix}{\mspace{79mu} {{R_{n}( {\rho_{i\;} + t} )} = {{G_{n}( {\rho_{i} + t} )} + {{F_{n}( {\rho_{i} + t} )}\frac{G_{n}( \rho_{i} )}{{R_{n}( \rho_{i} )} - {F_{n}( \rho_{i} )}}}}}} & (3.78) \\{\mspace{79mu} {where}} & \; \\{{F_{n}(x)} = {\frac{x\; \gamma_{n^{\prime}}}{\mu^{*}n}\frac{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}^{\prime}( {\gamma_{n^{\prime}}x} )}} + {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}^{\prime}( {\gamma_{n^{\prime}}x} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}}} & (3.79) \\{{G_{n}(x)} = {{- \frac{x\; \gamma_{n^{\prime}}}{\mu*n}}\frac{{{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{K_{n}^{\prime}( {\gamma_{n^{\prime}}x} )}} + {{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}{I_{n}^{\prime}( {\gamma_{n^{\prime}}x} )}}}{{{I_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{K_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}} - {{K_{n}( {\gamma_{n^{\prime}}( {\rho_{i} + t} )} )}{I_{n}( {\gamma_{n^{\prime}}\rho_{i}} )}}}}} & (3.80)\end{matrix}$

For the case when σ=0,

$\begin{matrix}{{R_{n}( {\rho_{i} + t} )} = {\frac{1}{\mu}\frac{1 - {\mu \; {R_{n}( \rho_{i} )}{F_{n}( \frac{\rho_{i} + t}{\rho_{i}} )}}}{{\mu \; {R_{n\;}( \rho_{i} )}} - {F_{n}( \frac{\rho_{i} + t}{\rho_{i}} )}}}} & (3.81) \\{where} & \; \\{{F_{n\;}(x)} = \frac{x^{n} + x^{- n}}{x^{n} - x^{- n}}} & (3.82)\end{matrix}$

3.3.5 Implementation and Validation

The implementation procedure for this model parallels the previousmodel:

-   -   1. Define the current density in the primary windings based on        knowledge of the sensor geometry and winding position and using        the uniform current density assumption discussed earlier. Take        the Fourier transform of the current density profile to        determine the wavenumber modes of the surface current density.    -   2. For each wavemode, start at the innermost and outermost        material interface and apply the transfer functions defined in        Section 3.4 to determine the surface reluctance density on        either side of the plane of the primary windings.    -   3. Calculate the magnetic vector potential in the plane of the        primary windings for each wavenumber mode using Equation 3.73.        Convert this to the magnetic vector potential in the plane of        the sense element using Equation 3.75.    -   4. Calculate the magnetic field for each wavemode at the sense        element using Equation 3.56.    -   5. Sum the magnetic fields due to each wavemode to determine the        total magnetic field at the sense element due to a unit current        excitation.

Since the procedure and equations are similar, the numericalimplementation in Matlab has many of the same issues. Because of some ofthe extra terms in Equations 3.56, 3.75, 3.79, and 3.80, the efficienttreatment of the Bessel functions is extra important. Taking intoconsideration the assymptotic nature of the modified Bessel function astheir argument gets large [6] saves much simulation time. This is theequivalent of using the Cartesian coordinate model for large ρ.

The sensor shown in FIG. 25 was used to validate this model. Because noscanner was available to validate that the required symmetries weremaintained after the sensor was wrapped around a pipe in thisorientation, much care had to be taken to assure that the sensor'sgeometry matched the assumptions of the model. Specifically, care had tobe taken to make sure that the sense elements remain in the samecylindrical plane as the drive wires when wrapped around the pipe.

A simailar measurement procedure was used to validate this model. FIG.29 and FIG. 30 show the results that validated the cylindrical modelimplementation. FIG. 29 shows that the model successfully predicts theair responses of the sensor when wrapped around plastic cylinders ofvarying diameters. The response of the sensor in air when flat (beforewrapping around the plastic cylinders) was normalized to 1+0j. Only themagnitude of the impedance response is plotted as the phase was alwayszero. The RMS error of the measured air responses as compared to themodel-predicted air responses is under 0.14%, which is within thetolerances of the experimental setup. FIG. 30 shows the results oftaking measurements on a 6.625″ diameter, 0.25″ wall thickness pipe atvarying lift-offs plotted on a lift-off/thickness grid. The air pointrepresents the sensor's response in air when at a diameter of 10.625″(6.625″ pipe+2″ of insulation). The data follows the lift-off line uptowards the air point. As the lift-off increased from 0.5″ to 2.5″, theestimated thickness varied only by ±0.004″, with estimates ranging from0.247″ to 0.254″.

SECTION REFERENCES

-   [1] N. J. Goldfine, “Uncalibrated, Absolute Property Estimation and    Measurement Optimization for Conducting and Magnetic Media Using    Imposed ω-k Magnetometry,” Doctoral Thesis, Cataloged into the    Massachusetts Institute of Technology Libraries, October 1992.-   [2] Y. Sheiretov, “Deep Penetration Magnetoquasistatic Sensors,”    Doctoral Thesis, Cataloged into the Massachusetts Institute of    Technology Libraries, June 2001.-   [3] D. Schlicker, “Imaging of Absolute Electrical Properties Using    Electroquasistatic and Magnetoquasistatic Sensor Arrays,” Doctoral    Thesis, Cataloged into the Massachusetts Institute of Technology    Libraries, October 2005.-   [4] H. Haus, J. Melcher, Electromagnetic Fields and Energy,    Prentice-Hall Inc., New Jersey, 1989.-   [5] F. Bowman, Introduction to Bessel Functions, Courier Dover    Publications, 1958.-   [6] F. Olver, L. Maximon, “Chapter 10: Bessel Functions,” Digital    Library of Mathematical Functions, http://dlmf.nist.gov/10, June    2013.-   [7] ASTM Std E-2338

Section D-C: Calibration

The inventors have recognized and appreciated the need for calibration,used in step 2001 and step 2007 of method 2000.

Sensor transimpedance data (Z) are obtained by applying a drive signalto the primary sensor winding. The resulting current in the primarywinding (l) and voltage across the secondary winding (V) are measuredand the transimpedance is calculated as the ratio of these twoquantities, i.e.,

Z=V/I  Equation 1:

It must be appreciated that all quantities discussed in this section arecomplex numbers, since in the sinusoidal steady state (SSS) regime,under which impedance analyzer 117 is operated, every signal ischaracterized by two values: a magnitude and a phase angle, or,equivalently, the real and imaginary components of a complex number.

In physical implementation, certain parasitic effects interfere with theability of impedance analyzer 117 to measure V and I accurately.Therefore there is a need for a method to obtain Z from I_(m) and V_(m),which are the measured values of I and V, respectively.

The parasitic effects can be grouped in one of three classes, dependingon how they contribute to the measured quantities.

Class 1: Scale factor. A number of different phenomena manifestthemselves as scaling of the signal, i.e., multipliplication of thevoltage and/or current measurement by a complex number. For example, theinstrumentation electronics have an overall gain and phase shift. Asanother example, the same model can be used for sensors that differ onlyin the length or number of secondary components, resulting in differentmultiplicative factors for each sensor. Cables can also introducescaling and phase shift due to losses and to unmodeled capacitance orinductance of the cable. Since the scaling factor is a complex number,it can represent both scaling of the magnitude and changes in the phaseof the signal.

Class 2: Parasitic coupling. Some of the measured voltage is the resultof effects other than those due to the transimpedance of the sensor. Forexample, voltage can be induced in the secondary winding leads by themagnetic field of the drive winding or its leads. Furthermore,electronic components of the drive and sense electronics are located inclose proximity and can couple to each other. This parasiticcontribution to the voltage signal is proportional to the current Ithrough the sensor. Note that it is theoretically possible to haveparasitic voltage that is independent of I, or proportional to I_(m)rather than I. Such effects are not observed in practice and are notaddressed by this method.

Class 3: Parasitic current. The electronic components that measure thecurrent can have a parasitic component, i.e., output a non-zero valueeven when the current though the sensor is zero. This is again due tonon-ideal behavior of electronic components.

The parasitic effects can be represented by Equation 2 and Equation 3.

$\begin{matrix}{I_{m} = {I + I_{p}}} & {{Equation}\mspace{14mu} 2} \\{V_{m} = {\frac{1}{K}( {{ZI} + {Z_{p}I}} )}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

In Equation 3, Class 1 effects are represented by the scaling factor1/K. Class 2 parasitic coupling is represented by transimpedance Z_(p).In Equation 2, Class 3 effects are represented by the parasitic currentI_(p). Equations 1, 2, and 3 are combined to obtain Equation 4 that isused to obtain Z from I_(m) and V_(m).

$\begin{matrix}{Z = {{K( \frac{V_{m}}{I_{m} - I_{p}} )} - Z_{p}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

The calibration method constitutes application of Equation 4 to rawimpedance data. It is therefore necessary to obtain the values of thethree parameters K, Z_(p), and I_(p). This is accomplished using Method3100 in FIG. 31.

To obtain the parasitic current I_(p), a measurement is taken with thesensor disconnected. In this case the parasitic current I_(p) is equalto the measured current I_(m). This is accomplished in steps 3101 and3103. Step 3105 is used to obtain K and Z_(p). There are severalpossible methods for carrying out step 3105. These are methods 3200,3300, 3400, 3500, and &3600, illustrated in FIG. 32, FIG. 33, FIG. 34,FIG. 35, and FIG. 36, respectively. Though, other suitable methods maybe used in step 3105. The choice between these methods depends on theapplication.

It must be appreciated that if parasitic current I_(p) is zero, or ifthe effect is ignored, then steps 3101 and 3103 of method 3100 may beomitted.

Methods 3200, 3300, 3400, 3500, and 3600 contain steps wheremeasurements are taken in different configurations. The outcomes ofthese measurements are used by subsequent steps and are represented astransimpedance values Z_(m) defined in Equation 5.

$\begin{matrix}{Z_{m} = \frac{V_{m}}{I_{m} - I_{p}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

With this definition, Equation 4 can be written as Equation 6.

Z=KZ _(m) −Z _(p)  Equation 6:

Methods 3200, 3300, 3400, 3500, and 3600 contain steps where simulatedimpedance values, a.k.a. precomputed sensor responses, are obtained froman analytical model, which computes the sensor's transimpedance in air(Z_(a)) or on reference materials (Z_(r)), as indicated in the flowcharts. These precomputed sensor responses can be obtained byinterpolating into a precomputed sensor database (PDB), or by directapplication of the model. Since the methods can incorporate more thanone measurement or simulation, numerical subscripts will be used todifferentiate between them.

Method 3200, Air Calibration, is illustrated in FIG. 32. In this methoda single data point is taken with the sensor in air. Since onemeasurement does not provide enough information to compute twoparameters, only K is computed and the parasitic impedance Z_(p) is setto zero. This method is appropriate when Z_(p) is known to benegligible. The CUI application uses this method. Equations 7 and 8 areused by Method 3200.

$\begin{matrix}{K = \frac{Z_{a,1}}{Z_{m,1}}} & {{Equation}\mspace{14mu} 7} \\{Z_{p} = 0} & {{Equation}\mspace{14mu} 8}\end{matrix}$

Method 3300, Air/Shunt Calibration, is illustrated in FIG. 33. Inaddition to a measurement with the sensor in air, this method alsoincludes a measurement in air with a “shunt”, which is a constructidentical to the sensor except that the secondary windings are notconnected to the leads. Under these circumstances the transimpedance Zis zero, effectively allowing for a direct measurement of Z_(p), whichis a scaled version of the impedance measured with the shunt. Equations9 and 10 are used by Method 3300.

$\begin{matrix}{K = \frac{Z_{a,1}}{Z_{m,1} - Z_{m,2}}} & {{Equation}\mspace{14mu} 9} \\{Z_{p} = {KZ}_{m,2}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

Method 3400, Air/Shunt/Shunt-on-Part Calibration, is illustrated in FIG.34. This is a variation of Method &501. K is calculated in the same wayusing data from the first two measurements. A third measurement step isadded, with the shunt placed on the object under test. The parasiticimpedance Z_(p) is calculated using data from this third measurement.This method is appropriate in situations where Z_(p) is affected by thepresence of the object under test. Therefore, one shunt measurement inair is needed as part of determining K, and one shunt measurement on thepart is needed to determine Z_(p) in the presence of the object undertest. Equations 9 and 11 are used by Method 3400.

Z _(p) =KZ _(m,3)  Equation 11:

Method 3500, Single-Part Reference Calibration, is illustrated in FIG.38. This is a variation of Method 3200, but instead of a measurement inair, the measurement is taken on a reference material or object, whoseproperties are expected to be similar to the test object. As in Method3200, the parasitic impedance Z_(p) is set to zero. For example, thismethod can be used in situations where the sensor cannot easily beremoved from the scanning fixture. Equations 8 and 12 are used by Method3500.

$\begin{matrix}{K = \frac{Z_{r,1}}{Z_{m,1}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Method 3600, Reference Calibration, is illustrated in FIG. 36. Ratherthan obtaining Z_(p) from a shunt measurement, as was done in methods3300 and 3400, in this method Z_(p) is computed indirectly,simultaneously with K, from measurement data with the sensor on two ormore different reference material systems. Equation 6 is used once foreach measurement, resulting in the matrix equation 13.

$\begin{matrix}{{\begin{bmatrix}Z_{m,1} & {- 1} \\Z_{m,2} & {- 1} \\\vdots & \vdots\end{bmatrix}\begin{bmatrix}K \\Z_{p}\end{bmatrix}} = \begin{bmatrix}Z_{r,1} \\Z_{r,2} \\\vdots\end{bmatrix}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

K and Z_(p) are obtained by solving the matrix equation 7. Note that ifmore than two reference measurements are used, Equation 13 will not, ingeneral, have an exact solution, in which case it must be solved in theleast-squares sense, where the error is minimized.

Note that the two or more reference systems may differ only in thelift-off, i.e., the distance between the sensor and the referencematerial. In one embodiment, “shims”, i.e., magnetically inert films ofa known thickness, are used to provide a different lift-off for eachreference measurement.

When calibration data on reference material systems is taken, to be usedin methods 3200, 3300, 3400, 3500, and 3600, it is necessary that thereference systems be constructed in a way that matches the assumptionsused by the analytical model. Specifically, if the model assumes acylindrical geometry, e.g., for CUI measurements on pipes, then when thecalibration data is taken in air, the sensor must be bent to follow acylindrical surface with a radius matching the radius of the sensor whenit is used on the pipe. Whereas it is possible to use a flat surface anda corresponding flat surface model to obtain calibration parameters,more accurate calibration will be achieved when the same sensorconfiguration is used to obtain calibration and measurement data.

Flaw Sizing

While the double-rectangular sensor design provides a morerepresentative flaw response with minimal impact from unmodeled effects,the resulting response is still a “blurred” image of the actual flaw.Hence, the MR-MWM-Array approach to CUI requires an algorithm to provideaccurate sizing information for detected flaws. The following describesMethod DDD and demonstrates its successful implementation.

Proposed Lattice Approach for Flaw Sizing

By taking the computed footprints generated in the previous chapter andconvolving them with simulated defects of various sizes, we can create amultidimensional database that can be used along with JENTEK'smultivariate inverse methods, also known as grid methods, to produceflaw sizing estimates. JENTEK's grid methods are typically used toconvert multifrequency transimpedance measurements into absolutematerial properties: for each frequency measured, the real and imaginarycomponents of the impedance response provide two equations. Givensufficient selectivity (independent equations are provided by themultifrequency impedance data), n frequencies allow for the estimationof 2^(n) properties. The sensitivity and selectivity of a measurementcan be analyzed using singular value decomposition of the Jacobianmatrix [N. J. Goldfine, “Magnetometers for Improved MaterialsCharacterization in Aerospace Applications,” Materials Evaluation, vol.51, no. 3, pp. 396, March 1993].

It is necessary to find a set of observable measurement characteristicsthat can be used to correlate to the flaw characteristics of interest.Since flaws can come in all shapes and depth profiles, assumptions needto be made about observed flaws. If each flaw is assumed to be discreteand of uniform depth over a rectangular area, then the flawcharacteristics to be measured are well defined: length, width anddepth. Therefore, it is necessary to determine three observablemeasurement characteristics for each flaw.

Length is defined to be in the circumferential direction of the pipelineand width is defined to be in the axial direction of the pipeline.Length and width can also be characterized relative to the sensor;length is in the channel direction and width is in the scan direction.

The proposed measurement characteristics can be determined using thefollowing procedure for Method DDD:

Apply a threshold to the thickness image to identify the location ofdiscrete flaws.

Determine the location of each discrete flaw and an estimated length andwidth of the response that exceeds the threshold.

Within the area of the flaw, determine the maximum flaw response.

Using this procedure, the generated flaw sizing lattice has three inputsand three outputs. The inputs are flaw response length and width below agiven threshold, and maximum flaw depth. The outputs are estimated flawlength, width and uniform depth.

Lattice Generation and Orthogonality

In order to prove the validity of Method DDD, it is necessary to firstgenerate a test lattice with sufficient sensitivity and selectivity togenerate reliable flaw characteristic estimates given measuredobservations. For the following discussion, the inputs to the lattice,dependent variables in the forward model (measured signal width, lengthand uniform depth), will be referred to as as signal characteristics,and the outputs of the lattice, independent variables in the forwardmodel (estimated flaw width, length and uniform depth), will be referredto as flaw characteristics.

Sensitivity measures the resulting change in flaw characteristics due tosmall changes in signal characteristics. Low sensitivity (i.e. verylarge changes in flaw characteristic due to a perturbation) can resultin a very unreliable measurement. A lattice's selectivity reflects theindependence of the lattice's output parameters. A low selectivitylattice results in the lattice being multivalued (a set of measurementcharacteristics corresponding to more than one possible set of flawcharacteristics) which causes the multivariate inverse method searchalgorithm to fail.

The sensitivity and selectivity of the lattice can be evaluated byvisualizing the three-dimensional lattice in multiple two-dimensionalslices. This is shown in FIG. 38 for a flaw sizing lattice generatedwith an 0.015″ threshold using the footprint generated by Method CCC forthe sensor pictured in FIG. 43. The nominal pipe diameter was 6.625″ andthe pipe wall was 0.280″ (this is a standard 6″ schedule 40 pipe size).The flaws were assumed to be internal flaws, although the lattice changeis minimal when external flaws are considered.

The selectivity of the lattice can be evaluated by looking at the linesof constant flaw characteristic property and looking to see if they areclose to orthogonal to the other lines of constant flaw characteristicproperty (for example, seeing if a line of constant flaw length andwidth while varying depth is orthogonal to lines of constant flaw lengthand depth while varying width). If the lines are close to beingparallel, then there is low selectivity and the nonlinear searchalgorithm will be unstable. In all three grid slices that are displayedin FIG. 38, the selectivity above a flaw width of 1″, length of 1.5″ andflaw depth of 0.040″ should be sufficient for successful implementation.

Sensitivity can be determined by the size of the grid cells seen in thethree slices displayed in FIG. 38. Again, the sensitivity seemsacceptable above the same flaw sizes determined to be sufficient forselectivity.

Below these selectivity and sensitivity limits, it is unlikely that theflaw sizing algorithm will be reliable. However, these limits showfeasibility for the algorithm to be able to size flaws that meet theapplication requirements. Given acceptable sensitivity and selectivity,since the lattice is not overconstrained (the number of inputs andoutputs are equal), it follows that if the observed sensor responsefalls within the lattice, then there may be a unique solution.Furthermore, while sizing may not be reliable for flaws smaller than thelimits defined in this section, detection still will be possible.

It is interesting that the selectivity and sensitivity are acceptable ata lower width threshold than length threshold. This makes sense, though,if we keep in mind that the footprint in the length direction is muchbigger for this sensor than in the width direction. Therefore, in thewidth direction we have more sensitivity to local defects and canresolve them at smaller sizes.

Furthermore, it makes sense that there is enough independence in thelength, width and depth of the flaws given the observed length, widthand maximum depth of the flaw response. Based on the method ofconvolution, we can intuit the relationship between the input parametersof the lattice and the output parameters. As the flaw width changes, wewould expect the width of the response and the depth of the response tochange significantly and the length of the response to change minimally.Likewise, as the length of the flaw changes, we would expect the lengthof the response and the depth of the response to change significantlywhile the width of the response changes minimally. And finally, if thedepth of the flaw changes, we would expect all three responsecharacteristics to change. These three relationships would appear to beindependent.

While this visualization shows feasibility, the accuracy of the methodis still in question. This is analyzed in the following section.

Finite Element Method (FEM) and Measurement Validation of SizingApproach

Using the footprint convolution method for sizing requires a morestringent validation. The width, length and depth of a sensor's responsemust match the result of convolving the sensor's footprint with asimulated flaw to an accuracy that allows the multivariate inversemethods to effectively use the generated lattice.

Since it is not practical (from both a cost and time perspective) tocreate a large number of sample flaws of varying sizes and depths, FEMsimulation was used to predict the response of the sensor pictured inFIG. 43 to an array of flaw sizes and depths in flat steel plates 0.25″thick with 2″ of lift-off. These simulations used the commercial packageFaraday, a three-dimensional eddy current solver from IntegratedEngineering Software. The boundary element method was used with thispackage to determine the magnetic field distributions since it does notrequire as much memory or processing time as finite element modelpackages. These simulations used a self-adaptive mesh with an accuracysetting 0.0003 to refine the mesh density for the computation in theareas where the fields were changing relatively rapidly and anaccuracy/speed factor of 3. A smaller accuracy setting or a larger speedfactor reduces the numerical error in the calculation at the expense ofusing more memory and a longer processing time; previous work had shownthat settings that were used were reasonable for this geometry. Notethat typically 2-8 GB of RAM were required for these simulations.

Because FEM simulations converge very slowly, simulating a scan over asingle flaw would take nearly a month of computation time (15 minutesper measurement, 0.5 inch measurement spacing, 24 by 24 inch measurementgrid, 8 flaw sizes, 10 flaw depths). A more practical use of FEMsimulation for validating the footprint convolution sizing method is tosimulate only the point of maximal response for each flaw. Since boththe footprint model and initial measurements agree on the position forthis maximal response this is a reasonable approach. 20 Hz was thesimulation frequency.

FIG. 39 and FIG. 40 summarize these results. What we see is goodagreement between the simulated measurements and the footprint modelconvolution for flaws of varying sizes and aspect ratios: there is alinear relationship between flaw depth and response maximum, and theslope is determined by the area of the flaw. However, the linearity ofthe FEM simulations starts to break down for the small aspect ratioflaws with large depth. This is likely due to a numerical noise issue inthe FEM simulation: it was difficult to get convergence in these cases.

With demonstrated agreement between the models and the simulatedmeasurements, and a lattice that has reasonable sensitivity andselectivity, the final verification step is to try to process actualmeasurements. A 4″ long (circumferential), 6″ wide (axial), 0.100″ deepflaw in a 6.625″ diameter, 0.280″ thick pipe was scanned with 2″ ofinsulation and standard weatherjacketing. The flaw response, shown inFIG. 41 (left) was thresholded with a 0.015″ threshold, and thethresholded image is shown in FIG. 41 (right). The flaw response had ameasured length of 5.3″, width of 5.9″ and maximum depth of 0.0248″.These numbers were processed through the footprint sizing lattice andthe estimated flaw size was very reasonable. Perturbations were appliedto the measurement responses to verify acceptable sensitivity andselectivity of the lattice. Small changes in response sizes resulted inacceptably small changes in flaw estimate size. These results aresummarized in FIG. 42.

Section E: Applications

Section E-B: In-Line Inspection (ILI)

In-line inspection (ILI) devices are a type of tool configured fortraveling inside of a pipe or pipeline. One type of ILI tool isconfigured to identify locations of pipe wall loss due to corrosionwithin a pipe based on the principles of magnetic flux leakage (MFL).These tools offer the state of the art performance for inspection ofboth liquid and gas pipelines using magnetic fields. However, they havemany limitations. The MFL mode provides both internal and externalcorrosion imaging capability and very limited crack detectioncapability. Using a constant field produced by permanent magnets and anarray of hall sensors located to provide circumferential coverage and tomeasure the magnetic field response at each circumferential location, arelatively high-resolution corrosion image is achieved as the tooltravels axially down a pipeline. Recent advances include dual fieldmodes implemented by Rosen, but similar to the dual spatial wavelengthand segmented field methods described by Melcher and later by Goldfinerespectively; the dual orientation methods, or single orientations(e.g., at 45 degrees) to detect both axial and circumferential cracks,implemented by TDW, but also previously introduced by many for otherapplications, including by Goldfine. The eddy current mode introducedover the last decade by many offers high resolution internal geometrymapping, but in the implemented format is limited by the eddy currentwinding construct, electronics architecture, and data analysisalgorithms used.

Major limitations for the MFL mode include (1) the need for the magnetsto provide near saturation level fields and therefore needing large andheavy magnets and introducing difficulties associated with largemagnets, such as the potential to become lodged in the pipeline andvariation in magnet strength, (2) poor modeling of the physics due tothe inclusion of difficult to model field constructs resulting indifficult data interpretation, (3) relatively poor crack detectioncapability because of wide spacing of the hall sensors and thedifficulty of detecting cracks (such as tight internally initiatedcracks) with a constant field mode even with two orientations, (4) falseindications caused by inconsequential magnetic anomalies in thematerial, and (5) poor defect sizing due to limited availableinformation from the MFL mode even with dual orientations or dual fieldmodes.

Poor defect sizing is alleviated slightly by the combined use of theeddy current and MFL modes, but due to the limits of the implementededdy current mode, this is also limited. Conventional eddy currentsensing methods used with MFL tools have many limitations including (1)loss of calibration with variations in magnetic permeability of the pipewall because the lift-off line orientations vary with magneticpermeability, (2) inability to properly scale material loss anomalies orcrack like features with lift-off due to curvature of lift-off lines andthe inability to properly determine the lift-off value, (3) cross-talkbetween closely spaced coils, (4) variation of response for defectsdirectly over a coil versus defects between coils, (5) difficultymodeling and predicting the sensor response for varied material undertest conditions and operating conditions, such as temperature, due tothe coil geometry selection, and (6) use of electronics that is switchedbetween sensing elements and that does not enable simultaneousmeasurement of both impedance magnitude and phase (or real and imaginarypart of the complex impedance, defined as the ratio of the sensingelement voltage to the drive current). The last limitation introducesboth coverage and data interpretation limitations that are severe forhigh speed tools.

Perhaps the biggest deficiency of both the MFL and conventional eddycurrent methods is the lack of reproducibility. Changes in the fieldstrength or changes in the gap between the sensing elements and the wallor the magnets and the wall, as well as tilting and off-centerpositioning of the tool so that all sensing elements are not equaldistance from the internal wall will produce variations in the MFL andconventional eddy current sensor responses. These variations make itdifficult to compare runs from past inspections with the currentinspection. It is common for service providers to find that corrosiondefects appear to get smaller (a physical impossibility) using thesecurrently available ILI tools.

Another major issue with ILI tools, including MFL tools, ultrasonictools and more recent EMAT tools is their length and ability to bereduced in size for small diameter pipeline inspections. The length andweight of these tools requires relatively long and costly “piglaunchers.” The weight, length and complexity of these tools requiresubstantial logistics support for transport and handling. Thus, thesetools are typically run on a pipeline once every 3-6 years. It is notpractical to run existing tools often, due to logistics costs, andrepeated runs cannot be practically compared for MFL tools due to lackof repeatability, and many pipelines sections do not have the requiredpig launchers.

Having appreciated these deficiencies, the inventors provide aminiaturized electronics configuration that provides fully parallelsensing element electronics and support for multiple synchronized driveconductor segments, allowing simultaneous measurement of the real andimaginary part of the complex impedance on numerous channels.

FIG. 44 shows an ILI tool 4401 within a pipe 4403 according to someembodiments. Tool 4401 includes a tool body 4402, with systemelectronics, a plurality of sensors 4411-4415, and support armatures4405. In some embodiments sensors 4411-4415 include a drive winding withan arc-shaped segment. The arc-shaped segment may be curved to match theinternal pipe diameter, but offset to account for the designed averagegap between the arc the internal surface of the pipe wall. Eacharc-shaped segment may include an independently driven drive winding andan array of sensing elements at a fixed distance from the drive. Forexample, an MWM®-Array sensor may be used. The drive winding may form asingle rectangle, a dual rectangle configuration, or any other suitabledrive winding configuration (see FIG. 3 of US Patent Publication No.2013/0124109). Those of skill in the art will appreciate that tool sizeconstraints, among other factors, may affect the selection of one drivewinding configuration over another.

Using a dual rectangle drive construct, two rows of sensing elements maybe incorporated into sensors 4411-4415 (one linear array within each ofthe two dual rectangles as shown in FIG. 3D of US Patent Publication No.2013/0124109). A precomputed database of sensor responses, similar tothat presented in Goldfine et al. (U.S. Pat. No. 5,629,621) and refinedin subsequent patents, may be used to estimate the lift-off between eachsensing element and the internal pipeline wall surface at each impedancemeasurement location, and the same precomputed database is used toestimate a second property of interest.

The second property of interest may be the magnetic permeability in thedirection perpendicular to the drive segment. In some embodiments thearc-shaped drive winding segment is oriented circumferentially (similarto FIG. 3G of US Patent Publication No. 2013/0124109) to estimate themagnetic permeability in the axial direction. In another embodiment, thearc-shaped drive segment is oriented at an angle, such as 45 degrees, toenable detection of cracks in both the circumferential and axialorientation and the measurement of stress components in both the hoop(circumferential) and longitudinal (axial) directions.

Two rows of sensors 4411-4415 may be included to enable full coveragecircumferentially and to allow the drive segment on each arc to extendbeyond the last sensing element to improve the model accuracy for themodels used to generate the precomputed databases. As illustrated inFIG. 44, sensors 4411, 4413, and 4415 form one row of sensors offsetcircumferentially from a second row formed by sensors 4412 and 4414. Ofcourse, other sensors, not shown in FIG. 44, may be present to completecircumferential coverage.

ILI tool 4401 may have flexibility to permit variation of pipecircumference, passing turns, curves, and other pipeline features. FIGS.45 and 46 illustrate how this flexibility may result in offset from thecenter of the pipe and tiling, respectively. Lift-off at each sensingelement may be used to determine both the location of the tool withinthe pipeline and the tilting of the tool. For example, in FIG. 45,lift-off 4501 and 4502 can be used to determine the offset of the tool4401 within the pipe 4403. Also, in FIG. 46, lift-off data at two ormore axial locations maybe be used to determine the tilt of the tool4401 within the pipe 4403. This information is in turn used to improvethe magnetic permeability estimates, accounting for the effects of thepipe wall curvature, the offset of the tool from the center of the pipe,the tilting of the tool and the retraction of the mechanical arms foreach individual arc.

System electronics of ILI tool 4401 may be configured to provide asingle relatively high frequency excitation sign to sensors 4411-4415.Here, a high-frequency is a frequency at which the depth of penetrationof the magnetic field into the material is less than 2 mm for pipes andthis is less than the wall thickness. The lift-off may be estimated ateach sensing element along with the magnetic permeability in thedirection perpendicular to the drive conductor arc-shaped segments, andthe lift-off is used to estimate the internal corrosion associated wallloss. The magnetic permeability may be used to detect cracks. The driveconductor oriented circumferentially allowing improved detection of seamweld defects and other axially oriented linear defects including cracksand lack of fusion. In another such embodiment, the drive conductor isoriented at 45 degrees to the pipe axis to enable detection of bothgirth weld cracks and seam weld cracks as well as other crack likedefects in circumferential and axial orientations. In another suchembodiment a meander drive or interdigitated rectangle drive is used tocreate a spatially periodic field around the circumference such that themeander drive longer winding segments are aligned axially so that theyare most sensitive to the magnetic permeability variations in thecircumferential direction. In one such embodiment the magneticpermeability is used to detect circumferentially oriented cracks. Inanother such embodiment the circumferential component of the magneticpermeability is used to estimate the hoop stress.

In one embodiment, the tool provides only a high frequency mode becausethe lower allowable frequency is constrained by the requirement toprovide high data resolution in the transit (axial) direction. The lowerallowable frequency is defined for this tool as being at a frequencyabove that needed so that one complete cycle for the drive current iscompleted within the tool transit time interval that allows the tool totravel a distance that less than the required axial data resolution atthe maximum anticipated tool speed. For example, if the maximum tooltransit speed is 20 meters/second, and the required data resolution inthe transit direction (axial) is 2 mm, then the minimum frequency ofoperation is 20 kHz. Under some special circumstances, impedanceestimation can be provided using half a cycle (period) to provide higherresolution, but this may result in a substantial data quality reduction.Given the lower allowable frequency and the skin depth associated withmagnetoquasistatic sensing field penetration into typical pipe steel,the inventors provide that this tool embodiment provides detection ofinternal corrosion, internally initiated cracks, internal stress andother such internal properties or defects of the pipeline material thatcan be interrogated with magnetic fields that are limited in their depthof penetration by the skin depth (or depth of penetration) of theapplied fields at the prescribed input current frequency. In oneembodiment of this invention, the miniaturized electronics and the useof precomputed databases allows the tool to provide sufficientreproducibility to provide a quantitative estimate of defect growthrates and to improve the confidence in defect sizing and detection byproviding multiple inspections of the same defect. In another suchembodiment the reproducibility of the data enables detection of changesin the pipeline magnetic permeability due to the stress conditionassociated with land movement, seismic events, mechanical damage, oroperations.

The value of providing a tool that can only detect internal defects andinternal stress condition is significant for applications whereconventional tools cannot provide the performance needed for suchdefects to ensure pipeline integrity. One example is sour gas pipelineswith variable elevation. For such sour gas lines, internal cracking andcorrosion can impact pipeline integrity. MFL tools require relativelyconstant speed and have limited detection sensitivity andreproducibility and require long pig launchers. Thus, for many such sourgas pipelines with variable elevation, tool speed cannot be sufficientlycontrolled and MFL performance is not sufficient. For such applications,there is a need for a tool that can be run frequently, providesreproducible results for internal defects and stress imaging that allowcomparison between runs for quanitative determination of the growth ofdefects and changes of stress conditions.

In one embodiment of the tool for internal damage and stress imaging, aswell as for other tool constructs, the position of the retractablemechanical arms and the lift-off measurement information is used toprovide the internal profile of the pipe for the purpose of assessingcorrosion, mechanical damage (such as dent size), and ovality of thepipe. FIG. 48 shows how the distance from the tool body to the pipe canbe estimated using the arm length (L), the arm angle (θ), the sensorliftoff (h), and the offset (c, which accounts for fixed portions of theassembly). By using multiple sensor heads placed around the tool bodyand by assuming the geometry of the tool body, the shape of the innersurface of the pipe can be estimated. Local changes in the inner surfacewould indicate corrosion, particularly if the change was radiallyoutward. Local changes that are radially inward or are associated withlarge permeability changes are likely mechanical damage sites. In onesuch embodiment, tilting of the tool is also accounted for using tworows of arcs that are offset axially both to allow full circumferentialcoverage as described earlier and to provide the estimation of the tiltangle relative to the pipeline centerline. This enables correction ofthe profile computation to provide improved estimation of dent geometry.In another such embodiment, the magnetic permeability measurementsprovided using the precomputed database described earlier are used toestimate the stress distribution at and near a mechanical damage site.

In one embodiment, the inventors provide a purely electromagnet drivenin-line inspection tool with no permanent magnets, but including an MFLemulation mode with constant fields, as well as an eddy current mode. Inthis case, constant means that a constant current is driven into a coilto produce a constant magnetic field. FIG. 49 shows a typicalconfiguration showing the eddy current sensors (4902) and two fixedcoils around the tool body (4901). The constant field may be produced bythe same drive windings as the eddy current sensors (4902) or by thefixed coils around the tool body (4901). The same winding (4902 or 4901)may be used to provide sinusoidal magnetic fields at one or moreprescribed frequencies. In some embodiments, one or more additionalwindings are included to provide additional field modes at prescribedfrequencies and at constant field, as needed to provide the informationneeded to characterize the defects of interest. For example, multiplefixed coils could be used to produce high fields and low fields tofurther characterize ID and OD defects. These fields could be producedon the same module or on a different module (each module is anindependent tool that are strung together to make a larger tool).

Bucking coils can be used to enable MR sensors to operate within thelarge fields. These bucking coils are coils of wire placed around thesensing elements. A current is driven into the coils such that the fieldproduced by the bucking coil cancels the field produced by the MFLemulation electromagnets.

In some embodiments, the power supply is recharged during operation.Recharging may be achieved by wheels riding along the inside of the pipewall to run a generator that charges the batteries. Alternatively, thegenerator may provide direct power through a power supply circuit.

In some embodiments, there is a single drive coil for multiple sensingelements, and the sensing elements are magnetoresistive. In another suchembodiment the sensing elements are of a different variety includinganisotropic magnetoresistors (AMR), giant magnetoresistors (GMR), hallsensors, inductive coils or other sensing elements for measuring one ormore properties of the magnetic field such as the magnetic fieldamplitude, phase, direction, or rate of change of the magnetic field.Sensing elements may be configured in an array to enable building ofimages. In some embodiments the sensing elements are configured tomeasure the radial component of the magnetic field or the rate of changeof the magnetic field. In some embodiments the sensing elements areconfigured to measure the component of the magnetic field perpendicularto a linear drive conductor. In another such embodiment, two componentsof the magnetic field or the rate of change of the magnetic field aremeasured.

In another embodiment, each sense element has its own associated drive.FIG. 50 shows an example of a sensor that has a single drive winding(5001) and a single sense element (5002). In this example, multipleloops are connected in series to produce a single effective senseelement.

In yet another embodiment, dual rectangle drive conductors are used toprovide both the constant and prescribed frequency modes to enablehigh-resolution imaging and reliable detection of external defects,mid-wall defects, and internal defects including corrosion, cracks,mechanical damage and manufacturing anomalies—all of these either atwelds, near welds or away from welds in the base material. FIG. 51 showsthe dual rectangle drive conductor (5101) and the array of senseelements (5102). In this example, the sense elements are MR, butalternative sense elements can be used. A row of sense elements is shownin the center of each rectangle of the drive winding, although thesesense elements can be offset from the center.

In some embodiments, the windings are oriented circumferentially toenable imaging of longitudinal stresses by estimating the longitudinalmagnetic permeability using a multi-variate inverse method with aprecomputed database for estimating the lift-off, permeability and wallthickness or other sets of properties as needed. FIG. 52 shows a toolwith a circumferential drive (5201). This embodiment enables detectionof residual and applied stress variations associated with mechanicaldamage, welding and post weld heat treatment, land motion, elevation andelevation variations/land slope, and other sources.

A cylindrical coordinate model may be used to estimate parameters suchas sensor lift-off and pipe properties. For example, the model may beused to generate precomputed databases which are used in conjunctionwith multivariate inverse methods to process sensor data. Though, othermethodologies to estimate the parameters of interest from sensor datamay be used (regardless of whether they utilize a cylindrical coordinatemodel).

In using the cylindrical coordinate model, a correction factor may beprovided for circumferential and/or axial misalignment (i.e., lack ofconcentricity) of the tool within the pipe. As previously described, tworows of MWM-Arrays may be used in the determination of the axialmisalignment with the internal pipe wall. Similarly, the lift-off ateach sensing element may be used to correct for the non-concentricity ofthe tool with the internal pipe wall.

In another embodiment, the position and misalignment of the tool isestimated using the lift-off data estimated using a relatively highdrive frequency. This position information is used along with themultivariate inverse method and a constant field mode (which may be anMFL emulation mode or an alternative constant field mode) to providewall thickness estimation. A complete image of the tool position and thepipe wall is built for all inspected segments of the pipeline.

The MFL emulation mode replicates the results of conventional MFL tools,providing an alternate means of compliance with existing standards. Thefield needed to provide a sufficient MFL emulation mode is substantiallyreduced by replacing the MFL hall sensing elements with the moresensitive MR sensing elements. A low-field tool uses lower power in aconstant field mode (MFL emulation mode) to extend the time thatbatteries can operate without recharging or to limit the rechargingcapacity needed in the tool.

A tool adapted to provide the low-field mode may be configured toperform method 5400 shown in FIG. 54. In this mode, the magneticpermeability and the wall thickness of the pipe as well as the sensorlift-off are estimated from sensor measurements. In some embodiments,the high frequency is used to estimate the lift-off and provide a firstguess for the permeability. The magnetic permeability and the nominalwall thickness can be used to adjust the amount of field being generatedin order to minimize the power consumption. Then the constant fieldsensor response is used to estimate the thickness and correct thepermeability.

FIG. 53 shows the process for estimating the conductivity of the pipe. Afirst guess for the wall conductivity is used to determine wallthickness or it can be estimated using the nominal wall thicknessestimated in regions away from likely defects. In this nominal wallthickness method for conductivity estimation, the better the nominalthickness is known, then the less error is introduced into the otherproperty estimates.

In some embodiments a uniform layered media model is used for theinitial estimation of lift-off, wall thickness, and permeability andthen a stored database of numerically simulated defect responses is usedto correct the defect size estimates (e.g., the depth of a corrosiondefect or the length and depth of a crack). An empirical result set maybe used for the detect size correction instead of the numericalsimulations. In yet another embodiment, a calibrated formula is used tocorrect the defect size; for example, the formula may be the ratio ofthe effective sensor footprint size to the estimate defect surfaceextent.

In some embodiments method 5300 is used to correct the permeabilityestimates around a mechanical damage defect or a weld to provideresiduals stress estimates.

In one embodiment, the longitudinal stress is estimated using arelatively high frequency mode to estimate the residual stress at a weldto assess the post-weld heat treatment (PWHT). Stress assessment may beaccomplished using an eddy current sensor at a high enough data rate toobtain at least 4 data points within the weld heat affected zone. Atleast four data points are needed to provide shape characteristics ofthe stress variation associated with PWHT. Both the higher frequency andconstant current modes may be used to characterize the PWHT. In anothersuch embodiment the quality of the welding is assessed instead of thePWHT. The weld quality is assessed using the shape of the magneticpermeability response as the tool travels across the weld.Characteristics of the shape are used to assess the weld quality. In onesuch embodiment the maximum weld permeability and the width of responseat half the peak value are used to provide a measure of the weldquality. It has been shown in the past that such features correlate withlack of fusion or other such defects.

In some embodiments the electronics, processors, sensors, and storagemedia are miniaturized to fit into a single module suitable forintegration with a cleaning tool scrubber or utility PIG format. In thisembodiment, performance is compromised as needed to achieve a smallenough module size to enable access with normal cleaning PIG launchers,not the more complex inspection PIG launchers. For example, combiningmany of the electronic components onto a single circuit board (andeliminating the interconnections) reduces the size of the electronics.Reducing power consumption and using high energy density batteriesreduces the size of the batteries. Also, eliminating the magnets used intypical MFL tools provides more space in the interior of the tool.

A preferred means is to develop dedicated chip sets to furtherminiaturize the electronics and reduce power requirements. For example,the analog-to-digital converters, the processor, and the communicationsfunctions can be combined into a single chip that has a more desirableform factor. The cost of such an implementation is prohibitive but theconcept is included in the disclosed invention.

In one embodiment, structured waveforms (in terms of the drive currentor voltage) are used to drive the drive windings to achieve improvedwall thickness, magnetic permeability, or defect detection performance.One such structured waveform is a DC bias field with a single frequencysuperimposed. The impedance instrument independently measuring the DCfield response and the real and imaginary part of the transinductanceassociated with the single frequency. Another structured waveformfurther includes a second superimposed frequency to estimate the wallthickness of the pipe.

For robotic tools or slowly moving tethered tools, both MR and inductivesensing elements may be used, but for fast moving tools, the preferredmethod is inductive at high frequency drive current (e.g. providingshallow penetration) and using a very high data rate for recording forthe sensor impedance (or transinductance measurements). In someembodiments filtering is included near the sensor for data taken at ahigh data rate to improve the signal to noise.

In one embodiment for estimating permeability and conductivityindependently for the pipe wall, the constant field and both a lowfrequency and higher frequency mode are used to provide independentestimates of the liftoff, conductivity, permeability and pipe wallthickness. This four unknown problem requires two frequencies and theconstant field mode. Since the impedance measurement requires a fullperiod, the data rate at the lower frequency will be very low, whichwill produce very coarse data density. The property estimates producedby the low frequency can be used by the constant field and highfrequency modes to provide improved defect size estimates.

In another embodiment, other complex excitation modes are used. In onesuch embodiment, a constant ramp of current is used with two separateILI tool modules that excite a saw tooth ramp so that one ramp is alwaysvarying with a constant slope to enable complete internal coverage. Theramp mode is unique in that it enables the penetration of the wall, butthe first derivative of the field is constant, thus the eddy currentpatterns and the inductive coil response are simplified. In this mode,the two separately excited ramps must be synchronized and out of phase.The advantages of this mode are both the simplified eddy currentpatterns and the ability to provide high data rates, as with MFL, butstill excite the eddy currents to improve defect sensitivity. For crackdetection, this mode is of particular value since eddy currents can beinduced throughout the wall thickness enabling higher sensitivity tolinear crack like defects. This is of particular interest for ERW pipeseam welds and girth weld cracks.

For crack detection, the orientation of the array relative to theorientation of the crack will affect the magnitude of the response. InFIG. 47, scan orientation 1 shows the scanner traveling in the samedirection as the length of the crack with the drive winding orientedperpendicular to the crack, which will provide the highest sensitivityto single cracks. For crack clusters (two or more cracks in closeproximity), the crack response from the two cracks will combine if thecracks are too close together. Scanning at an angle relative to thecrack length will decrease the magnitude of the crack response, butincrease the effective resolution of the scan. This increased resolutioncan be used to differentiate between cracks and provide independentmeasurements of crack location and crack depth. In FIG. 47 scanorientation 3 shows the scanner traveling in the same direction as thelength of the crack with the drive winding oriented at 45° to the crack.Another methods is shown in FIG. 47, scan orientation 3, where thescanner traveling perpendicular to the length of the crack with thedrive winding oriented at 45° to the crack.

Section E-I: Thin Sheet Inspection

FIG. 62 shows a system 6200 for inspecting a thin sheet of conductingmaterial 6202. The system includes an instrument 6203, sensor 6205, andmotion encoder 6204 that may be similar to instrument 110, sensor 120and motion encoder 143 shown in FIG. 1.

Thin sheet 6202 may be moving relative to sensor 6205 as indicated byarrow 6208. Arrow 6208 indicates the scan direction. In someembodiments, such as that shown in FIG. 62, thin sheet 6202 movesperpendicular to the direction of an array of sensing elements 6207 insensor 6205. In some other embodiments, sensing element array 6207 is atan angle with respect to the scan direction of thin sheet 6202 (e.g., 45degrees). Encoder 6204 may record the movement of thin sheet 6202 andinstrument 6203 may store the position of thin sheet 6202 in associationwith each sensor measurement and/or derivatives thereof (e.g.,properties, states, conditions).

A drive winding 6206 of sensor 6205 may be driven by instrument 6203with an electrical current at an excitation frequency which produces adepth of penetration (DOP) between 50% and 150% the nominal thickness ofthin sheet 6202. DOP is defined as follows:

D O P = 1/Re{Γ₁} where:$\Gamma_{n} = {{\sqrt{( {2\; \pi \; {n/\lambda}} )^{2} + {j\; {2/\delta^{2}}}}\mspace{14mu} {and}\mspace{14mu} \delta} = \sqrt{\frac{1}{\pi \; f\; \mu \; \sigma}}}$

In this equation λ is a characteristic length of a sensor, f is thefrequency of the input current, σ is the electrical conductivity of thethin sheet, n is 1, j is the imaginary unit, and μ is the magneticpermeability of the thin sheet. The characteristic length of a lineardrive eddy current sensor is defined as 4 times the distance between thelinear drive portion of the drive winding and the center of the sensingelements.

FIG. 64 shows a plot 6400 showing the depth of penetration as a functionof frequency for several characteristic sensor lengths and materials.Note that plot 6400 is a log-log plot.

In some embodiments of system 6200, sensor 6205 has drive winding 6206in the form of a single rectangular winding and the elements of sensingelement array 6207 are rectangular coils of one or more turns that arearranged in a linear array within drive winding 6206. In someembodiments, drive winding 6206 also includes a second rectangularwinding adjacent to the first, as shown in FIG. 65 for dual rectanglearrays 6501, 6502, and 6503 with the windings connected in series sothat the current in the closest drive segments are in the samedirection. A second array of sensing elements, 6504, may be includedwithin the second rectangular winding, in addition to the first sensingelement array, 6505, for each of multiple dual rectangle sensor 6501,6502 and 6503. The multiple dual rectangle sensor arrays may be arrangedto cover the width of the thin sheet as shown in FIG. 65.

The thickness and relative speed of thin sheet 6202 along with thesensor excitation frequency and sensor geometry may be used to determinethe resolution of system 6200 in the scan direction. The resolutionperpendicular to the scan direction will be determined by the elementspacing in the eddy current array, 6206.

As described above instrument 110, may be configured to provide atransimpedance measurement for each cycle of the excitation current. Thelowest excitation frequency will therefore drive the resolution of thesystem in the scan direction. For example, for a sheet moving at 10meters per second and a 10 kHz lowest excitation frequency, a dataresolution of 1 mm in the scan direction may be achieved. Resolutionrequirements may be prescribed by the operator or determined based ondetection sensitivity for a given defect type and minimum size. Todetermine sensitivity computer simulations or empirical data can beused.

The resolution may be improved in the scan direction by reducing the DOPrequired to perform the inspection or by modifying the materialproperties of thin sheet 6202.

The DOP required to perform the inspection may be reduced by inspectingfrom both sides of thin sheet 6202. FIG. 63 shows a system similar tosystem 6200 which additionally includes a second sensor below thin sheet6202. The sensors may be provided at the same location (as shown in FIG.63) as the sheet moves past the sensor or offset from one another in thescan direction. Where the sensors are aligned, the lift-offs from eachsensor may be measured and subtracting from the total gap between thesensors to determine the thickness of the sheet. The total gap may becontrolled mechanically such that it can be treated as a constant duringdata processing. Interference between the sensors may be reduced byoperating the upper and lower sensors at different excitationfrequencies. Though in some embodiments the two sensors are aligned andthe same excitation current is provided in both drive windings.

In some embodiments a constant magnetic field is provided near thesensors and thin sheet 6202 such that the magnetic permeability of thesheet is substantially reduced. As can be seen from the DOP equation, areduction in the magnetic permeability will increase the depth ofpenetration.

In one such embodiment the lowest frequency is increased to the highestvalue with a depth of penetration between 0.5 and 1.5 times the sheetthickness such that sufficient sensitivity is provided for the smallestdefect size that must be detected. Here, sufficient sensitivity isdefined as the signal to noise ratio at which the detection of thesmallest required defect is provided with approximately 90% probabilityof detection and high confidence of over 80%. In one such embodiment ameans is also provided for estimating the defect size. One such meansfirst characterizes the defect as near side, far side or through wall.Then assuming a defect geometry a database of defect responses is usedto estimate the defect size using the sensing element responses.

A method is provided for detecting small defects in the thin sheet wheresmall sensing elements of 1 mm by 1 mm are provided to form the arrays.The impedance response is provided for each sensing elementsimultaneously and a precomputed database of sensor responses is used toconvert the highest frequency impedance data to an estimate of thedistance between the sensing element and the nearest surface of theconducting sheet under test. In one such embodiment the same databasefor the highest frequency is used to estimate a property of the sheet,such as the conductivity (assuming a constant magnetic permeability) orthe magnetic permeability (assuming a constant conductivity). In onesuch embodiment the highest frequency is selected so that the depth ofpenetration at that frequency is substantially less than 0.5 times thethin sheet thickness. In one such embodiment with at least twofrequencies, a precomputed database and the lift-off (proximity)estimate from the highest frequency are used to convert the lowerfrequency data into estimates of the thickness of the thin sheet and thevalue of another property of the sheet, where the property may be themagnetic permeability of the sheet with an assumed constant electricalconductivity. In another such embodiment the thickness is estimated by aseparate means at one location and subsequently, using the thicknessestimate, the conductivity at this and other nearby locations isestimated independently from the magnetic permeability. Multiple suchlocations with alternative thickness measurements are then used toprovide electrical conductivity values for the entire sheet beinginspected.

In one embodiment the magnetic permeability in the directionperpendicular to the longer drive segments is also used to estimate thestress in the thin sheet. This is possible with all sensorconfigurations described for the thin sheet measurements.

In one embodiment of the above inventions the sheet is formed into apipe and the sensor arrays are located inside the pipe and the sensorsare traveling, as opposed to the thin sheet. In this invention thesensor array is mounted on an in-line-inspection tool.

It should be appreciated that while an apparatus and method have beendescribed in connection with a thin film that embodiments may address avariety of conductive layers such as pipes, pipelines, panels, and thelike.

In some embodiments of system 6200, the electrical current provided byinstrument 6203 simultaneously provides a second excitation frequencythat is higher than the first frequency. In one such embodiment thelowest frequency provides sufficient data resolution in the sheettransit direction to detect the minimum defect size of interest or toprovide the desired data resolution. The second frequency provideshigher sensitivity to near side defects and enables differentiationbetween through thickness and near side and far side defects. In oneembodiment a far side defect is detected only by the lower frequency,while near side and through wall defects are detected at bothfrequencies. In one such embodiment the ratio of the response at the twofrequencies for a property estimated from the response, such as themagnetic permeability, is used to differentiate through wall from nearside defects.

In one embodiment illustrated in FIG. 66 a precomputed database ofsensor responses is used at one or more frequencies to estimate thelift-off, and a property of the thin sheet 6202. In one embodiment twosensors on opposite sides of the thin sheet as illustrated in FIG. 63and FIG. 67 are synchronized so that the field from each sensor is inthe same direction as shown in FIG. 67.

The first lower frequency and second higher frequency from both arraysmay be used to estimate the magnetic permeability of the sheet with anassumed constant conductivity, and the magnetic permeability is used todetect defects and estimate their size.

A second higher frequency may be included and a two frequencymultivariate inverse method is used to estimate the thickness of thesheet, one electrical property and the lift-off distance between thesensing element and the near surface of the sheet, all at each sensingelement location.

The electrical property may be the magnetic permeability and theelectrical conductivity is assumed to be a constant value for the sheet.The electrical conductivity may be determined by measuring on a sampleof material from the same lot. The method used to measure the sample maybe a four point probe method that accounts for the sheet thickness.

The above may be configured as a stationary inspection apparatus formeasuring stress in a thin sheet moving relative to the inspectionapparatus. The inspection apparatus may include a plurality of sensingsegments, each sensing segment having an array of sensing elements at afixed distance from a linear drive conductor; an impedance instrumenthaving

A signal generator configured to generate an electrical current at afirst excitation frequency, said signal generator electrically connectedto provide the electrical current to the drive conductor, and aplurality of parallel sensing channels, each sensing channel dedicatedto a sensing element of the plurality of sensing segments and configuredto simultaneously measure real and imaginary components of an impedanceassociated with the respective sensing element at the first excitationfrequency, and the response at each sensing element being convertedusing a precomputed database of sensor responses over the range ofproperties and lift-off of interest to estimate the lift-off distancebetween the sensing element and the near surface of the sheet and themagnetic permeability of the sheet at the at least one frequency. Acorrelation relationship may be used for converting the magneticpermeability to stress, where this relationship was determinedempirically using a sample of the sheet material and the same sensingarray construct used in the apparatus. The system may determine theelectrical conductivity of the sheet, said electrical conductivity thenbeing assumed constant for the sheet.

The electrical conductivity and magnetic permeability are determinedfrom a stationary sample of the sheet and are assumed to be constant forthe sheet being inspected. A second higher frequency is used to estimatethe magnetic permeability of the sheet with an assumed constantelectrical conductivity. The electrical conductivity is determined usinga four point probe method on a representative sample of the sheetmaterial and the method accounts for the sheet sample thickness. Asecond sensing array is included on opposite sides of the sheet and thegap between the two sensors is held constant and the lift-off at a thesingle frequency for each pair of sensing element, above and below thesheet, is subtracted from the total gap to determine the sheetthickness. The drive currents for the array above and below the sheetsare synchronized. The frequency is selected so that the depth ofpenetration of the magnetic field produced by the drive current is lessthan 0.5 times the sheet thickness. A second frequency is simultaneouslyapplied to the drive conductor and the impedance at the two frequenciesis used to estimate the sheet thickness, magnetic permeability andlift-off using a precomputed database of sensor responses. The magneticpermeability is used to detect defects in the plate in addition tomeasuring thickness. The magnetic permeability is used to measure thestress in the plate in addition to measuring thickness. Applying aconstant magnetic field is performed by the system included at a fieldintensity sufficient to reduce the magnetic permeability by more thanhalf applying a constant magnetic field is included at a field intensitysufficient to reduce the magnetic permeability by more than half.Applying a constant magnetic field is included at a field intensitysufficient to reduce the magnetic permeability by more than half.

Section E-C: Weld and Post-Weld Heat Treat (PWHT) Assessment

Post-weld heat treatment (PWHT) is used to strengthen critical welds onpipes, pipelines and other structures. In this section it is assumedthat the structure is a pipe or pipeline, but it should be appreciatedthat the methods and systems described may apply to any welded materialstructure. Conventional PWHT assessment capability is limited tohardness testing on the outer surface of the pipe. This method cannotprovide a quantitative PWHT assessment after a weld has been purportedlyheat treated. Also, this method cannot provide an assessment of residualstresses for girth, seam, spiral welds or other welds or for the basematerial. Thus, pipeline operators must depend on documentation andworkforce skill to ensure quality of welds and PWHT. As documentationfor pipelines and other critical structures may not exist, be incompleteor inaccurate, a method for qualification of both welds and PWHT beforeburying of pipelines is needed. Once a pipeline is buried, the methodsand apparatus described in Section E-B may be used to enable inspectionof PWHT and weld quality from the inside using an ILI tool.

After welding to join two pipe sections using a girth (circumferential)weld, there are several zones of importance indicated by the pipe/weldcross-section 5500 of FIG. 55 taken in the axial direction. Starting atthe center of the weld is weld 5501 itself, and then moving axially awayfrom the weld there is the heat affected zone 5502 (HAZ), and continuingaxially there is the base material 5504. Furthermore, there are residualstresses in the hoop and axial directions that have been documented inthe literature both using models and experimentation. Hoop stresses arelargest at the center of the weld and then can continue beyond the weldand past HAZ 5502 into base material 5504. Base material and weldrelated stresses can be the results of the welding process, the pipemanufacturing process, construction or service. Thus, there is a weldingrelated residual stress affected zone 5503 (RSAZ) that includes weld5501, HAZ 5502 and some portion of base material 5504 on both sides ofweld 5501. Furthermore, if a PWHT is applied using a local heating coilsolution, the coil will have a width typically more than 5 times theweld width. Thus, for a one inch weld width with a 6 inch wide heatingcoil, the PWHT affected zone will cover 3 inches from the weld centerinto the base material.

FIG. 62 show a method 6200 of assessing PWHT and/or weld quality. Method6200 may be performed using a system such as system 100, shown inFIG. 1. Method 6200 may be performed at one or more sensor orientationsto perform the assessment based on may be used to assess PWHT and weldquality by image of the axial and/or circumferentially oriented magneticproperties of the material. Sensor 120 may be a sensor sensitive to themagnetic permeability of the pipe. The magnetic permeability of the pipemay be measured using a time varying magnetic field at one or moreprescribed frequencies. A database of precomputed sensor responses,generated using a model of the sensor and material under testinteraction, may be used to convert the response of sensor 120 into boththe magnetic permeability in the direction perpendicular to the drivewinding of sensor 120 and to the lift-off. This can be accomplished forthe weld and residual stress affected zone, as well as for the basematerial.

In some embodiments the change in magnetic permeability before and afterPWHT is used to determine if the PWHT was performed properly. Thisapproach may be used if the process is such that the change in magneticpermeability is dominated by the relaxation of detrimental residualstresses as a result of the PWHT process.

In some embodiments, the magnetic permeability is related to a measureof this residual stress in the pipe. The residual stress that remainsafter the PWHT process (or the change in residual stress before andafter PWHT) may be used to determine if deleterious stresses remain inthe pipe.

In some embodiments a library of spatial signatures (i.e.,characteristic sensor responses) are stored for both before and afterPWHT to determine features of the PWHT process for a given set ofprocess parameters (e.g, welding parameters, welding consumable, PWHTprocess, pipe material, pipe geometry and the like). A spatial signaturemay be measurements on a weld where the process parameters are welldocumented. Multiple spatial signatures may be generated by repeatingsuch measurement on many such welds (before and/or after PWHT). Thesignature may be further validated by alternative (e.g., destructive)testing that may not be practical in a field setting. Before PWHT andbefore welding the base material may also be inspected for residualstress from production of the pipe. In some embodiments the residualstress is inspected at low enough frequencies to measure residualstresses through the wall of the pipe at each inspection location andfor two or more drive winding orientations.

Features of the spatial signatures before and after PWHT may be computedfrom the sensor response and changes in these features are used toassess the PWHT quality and determine whether PWHT was performed or not.If it is determined that PWHT was performed an assessment of quality isalso possible. In addition, the library of spatial signatures andexperience is used to assess the confidence in the PWHT assessment, theweld quality assessment, and/or the residual stress estimation data.

In some embodiments the anisotropy of the magnetic permeability ismeasured by scanning with the sensor in two different orientations. Inone such embodiment the sensor is scanned with the linear drive first inthe circumferential orientation and then scanned again with the lineardrive in the axial orientation. In one such embodiment the anisotropy isdetermined in the region adjacent to the weld and on the weld and ananisotropy level below a prescribed level indicates that PWHT wasperformed. The prescribed level having been determined from scans onsamples that had been both properly PWHT and samples that did not havePWHT.

In some embodiments, features of the shape of the sensor response aretracked for many welds and the statistics of these features, possiblyfor thousands of inspected welds are recorded and stored. Thesestatistics are then used to determine if the population of welds, or asubpopulations, were welded correctly (for data taken after welding) orPWHT correctly (for data taken after PWHT). The data may be tracked overtime to look for changes in residual stresses after land motion orseismic events or after operation and long term service exposure,perhaps at high temperatures. This data is then used to supportdecisions regarding fitness for service, or as part of an overallpipeline integrity program.

In performing the above inspection a scanning fixture may be used toscan the sensor along the pipe with the sensor drive winding dominantlyin a prescribed direction. The scanning fixture may have wheels orientedto permit circumferential travel along the pipe. In some embodiments aframe is used to maintain an approximately constant distance to thecenter of the pipe and to enable smoother scanning at nearly constantspeed with a single motor. The drive winding orientation may becircumferential, axial or at an angle (e.g., 45 degrees). Thecircumferential and axial drive orientations will have greatestsensitivity to the axial and circumferential components of thepermeability, respectively. Positioning the drive winding at an angle ofcourse will result in a combined response.

In some embodiments the drive winding is excited at a frequency under200 Hz. Magnetoresistive sensing elements are used to providesensitivity deeper into the material than inductive elements and assessboth surface and subsurface residual stresses. Inspection may beperformed before PWHT to assess the weld quality and residual stressstate for the base material and after PWHT to assess the PWHT processand determine if deleterious stresses remain in the pipe. Though, insome applications it may not be possible to perform inspection beforePWHT (e.g., the PWHT may have already been completed). Measurements madeafter PWHT may be spatially registered with measurements taken beforePWHT.

For some embodiments the inspection can be performed through a coatingon the outer surface of the pipe.

In some embodiments an inductive sensing sensor may be used to achieve ahigher quality response to near surface residual stress andmetallurgical property variations with process parameters adjustedaccordingly as necessary (e.g., sensor excitation frequency).

The inventors provide an apparatus and methods for determining thequality of a weld that uses a mechanical scanner to move a conformablearray with a plurality of sensing elements and at least one linear driveconductor across the weld. This can be accomplished from either theinside or outside of a pipeline or on a flat or otherwise curved surfaceto inspect welds. In one such embodiment the sensors are mounted on anin-line inspection tool with multiple arcs that match the internalcurvature of the pipe. Each arc has a single rectangular drive conductoror a dual rectangle drive conductor and either one or two rows ofsensing elements located at the center of the one or two rectangles,respectively. In one such embodiment the tool moves at variable speeddown a pipe propelled by the gas product flow and impedance data isrecorded for at least one prescribed frequency. The goal is to provideweld quality assessment both with and without Post Weld Heat Treatment(PWHT). In one embodiment of this invention the goal is to provide anassessment of the stresses from the welding process either with orwithout PWHT. This stress at the welds is then used to determine thepipeline integrity and anticipate failures. Alternatively, this methodis used to identify susceptible welds and remove them by cutting themout or remove the stresses by applying PWHT only to those welds thathave excessive stresses.

In one embodiment of this invention an apparatus is provided where thesensing elements are inductive and the speed of the tool varies as thetool experiences varied pipeline elevation and the data rate is equal toa multiple of the time for a single drive current cycle at the lowest ofone or more prescribed frequencies and where a precomputed database ofsensor responses is used to convert the response at each sensing elementinto a magnetic permeability and lift-off value.

The inventors provide several different drive winding constructs eachwith a different purpose. In one such apparatus the linear driveconductor is oriented circumferentially and the magnetic permeabilityprovides a combined measure of both metallurgical changes and axialstress. In another apparatus multiple linear drive conductors areincluded at equal spacing around the circumference but are orientedaxially to provide a measure of the magnetic permeability in thecircumferential, hoop, direction. In one such embodiment these axialconductor segments form a meander drive or several smaller meanderdrives that are driven with a drive current at least one prescribedfrequency.

In one embodiment the magnetic permeability is correlated with stress inthe weld and the weld quality is assessed based on the tensile stressesnot exceeding a prescribed limit.

Section E-G: Crack Depth

Once a feature has been identified in the scans of an MWM-Array across atest material as a crack, it is useful to determine the length and depthof the crack since that affects remediation or disposition decisions.The crack length is typically obtained from the scan images of thesensor responses. The crack depth can be estimated from the previouslydeveloped correlations or analytical models for the sensor responses.The following provides a description of a method based on measurementsperformed on pipe sections with EDM notches of various known lengths,depths, and proximities. These current measurements establishcorrelation curves between the MWM responses and the notch depth andalso permit the generation of the hybrid measurement grids or latticesthat facilitate the rapid conversion of the MWM responses into depthinformation. A similar approach can be used with crack or notch modelsfor the sensor response instead of the correlation with measurementresponses.

To develop the correlation curves, measurements were performed on twosteel pipe sections that were fabricated with EDM notches. The samplespecimens are 3 ft long, 8 in. OD Schedule 40 and Schedule 80 steel pipesections. The specimens contained a series of notches of differentlengths and different depths. For the schedule 40 pipe, the isolated(single) notches had lengths of length 1.0 or 2.0 in. and depths thatvaried from 0.040 in. to 0.20 in. For the schedule 80 pipe, the isolatednotches have a length of 2.0 in. and depths that varied from 0.020 in.to 0.25 in. Both pipe specimens also contained 5 pairs of notches thathad different spacing between the notches and a depth of 0.040 in. forthe schedule 40 pipe and 0.080 in. for the schedule 80 pipe. Thisincluded three pairs of 1.0 in. long notches with spacings of 0.25,0.12, and 0.06 in. and two pairs of 0.5 in. long notches with spacingsof 0.12 and 0.06 in.

FIG. 56 shows a representative scan image of the effective permeability,obtained by processing the sensor responses through apermeability/lift-off measurement grid for an infinite half-space ofmaterial, for the schedule 80 pipe sample obtained with the FA24 at alift-off of 0.040 in. The FA24 was oriented with the drive windingperpendicular to the notch orientation; this orientation has the drivewinding oriented parallel to the hoop or circumferential direction ofthe pipe. These images assumed an electrical conductivity of 8% IACS andused an excitation frequency of 10 kHz. Similar results were obtained atother excitation frequencies up to 100 kHz, which is consistent withthese measurements being in a “high frequency” regime where the skindepth is small and the induced currents are essentially surfacecurrents. For both lift-offs, there is an increase in the effective (orapparent) permeability around the EDM notches and the magnitude of thechange varies with the depth of the notch. Slowly varying backgroundvariations in the permeability are also observed; these are typical ofas-manufactured steels.

FIG. 58 shows representative B-scan plots of the responses for severalchannels that were in or near the scan path for the deepest notches ofthe schedule 80 pipe. This plot shows that the background variations inthe permeability are small compared to the substantial increase in thepermeability observed for the sense elements that passed directly overthe notches. For this sensor there is a noticeable peak in the responseat the end of each notch response; this is associated with theasymmetric sensor design and the relatively large spatial wavelength forthis sensor array. This peak tended to be larger for the smallerlift-offs. Since the central portion of the response was observed to bemuch more representative of the notch depth than the end effectresponse, the central response was used when developing correlationsbetween the sensor response and the notch depth.

FIG. 57 shows an impedance view of a permeability/lift-off measurementgrid and the FA24 data at two lift-offs. This measurement grid assumedan infinite half-space of material and did not model the crack responseitself. The notch responses generally move in the same direction as thepermeability so the effective permeability provides a reasonableparameter to measure and correlate with the notch depths. For othermaterials and/or other excitation frequencies, it may be desirable tochoose a different parameter for correlating with the crack or notchdepth. The same type of response is observed at the higher lift-offs,but the absolute change in the impedance responses associated with thenotches are reduced since the sensor is farther away from the steelsurface. This can make the higher lift-off measurements more sensitiveto instrumentation noise and can also reduce sensitivity to the depth ofthe deeper notches since more of the sensing field drops across thelift-off layer. This implies that there is a balance where anintermediate lift-off can be chosen that will have both a reducedsensitivity to the end effects and also a reduced sensitivity toinstrumentation noise.

FIG. 59 (left) shows a representative correlation curve between theeffective permeability change and EDM notch depth for the MWM-Arraydrive winding oriented perpendicular to the notch length. The effectivepermeability change is obtained from the MWM-Array sense element thatpasses over the notch and is the difference in the average permeabilityof the notch response and the baseline permeability of the unflawedmaterial. The excitation frequency was 100 kHz and the nominal sensorlift-off to the steel pipe surface was 0.045 in. Similar results werealso obtained at 10, 40 and 63 kHz. Measured notch data for both pipesis presented. For single notches, there is generally a linear increasein the effective permeability with notch depth for this sensor array anddepths less than 0.25 in. This linear correlation is observed when thespatial wavelength is approximately twice the notch depth or larger.Otherwise, for small spatial wavelength sensors the effectivepermeability response can saturate and does not increase with depth forlarge depths. The slope of the correlation line tends to decrease as thelift-off increases, which suggests that smaller lift-offs are better toobtain greater sensitivity to the notch depth.

This plot also illustrates the effect of notch interactions. Theresponses to the pairs of notches show that interactions between thenotches increase as the spacing between the notches decreases. Thesignificance of this type of interaction is usually only significant forcrack clusters, as with SCC; the effect of the interaction is to causean overestimate of the depth when the responses from multiple shallownotches interact. Two approaches to reduce the effect of theinteractions are to scan with a higher spatial resolution MWM-Array andto rotate the MWM-Array to an angle such as 45°. FIG. 59 (right) showsthe permeability versus depth correlation curves obtained with the FA24oriented at a 45° orientation. For the single notch data, there was lessscatter in the data for the 45° orientation. This is also apparent inthe correlation coefficient values. The interaction effects are alsosmaller for the 45° orientation. This confirmed that the higher spatialresolution data obtained with the angled MWM-Array could improve theaccuracy of the depth sizing correlation.

For estimating the crack depths, the measurement data from scans withthe MWM-Array can be processed within the GridStation softwareenvironment using standard algorithms that solve for multiple unknownproperties from the appropriate measurement grids or lattices. Forexample, one instance of this algorithm analyzed used the measurementdata to estimate the permeability and lift-off. The scan image of thedata is then used to identify local property changes associated with thecracks, crack clusters, or notches. This also allows the backgroundpermeability of the pipe to be determined and can be used to confirmthat the lift-off is reasonable. This background permeability value isthen used as an input to a second multiple unknown algorithm that uses adepth/lift-off grid to provide the depth estimates. The results of thesecond application of the multiple unknown algorithm can be displayed inthe form of a scan image. As alternatives, the depth lattice can alsoinclude the sensor orientation and the background lift-off as latticeparameters. This would allow a single, albeit larger lattice, to be usedto accommodate a wide range of base material permeabilities, lift-offs,and sensor orientations.

FIG. 60 provides representative depth/lift-off measurement grids. Thesegrids represent slices of a permeability/depth/lift-off measurement gridlattice where the appropriate background permeability is chosen for eachpipe section. The depth/lift-off grid incorporates the correlationbetween the MWM response and the notch depth from the referencemeasurements performed on the pipe sections. In generating the grid, aninfinite half-space material model is used for preselected ranges of thebaseline permeability, depth, and lift-off. For each baselinepermeability, depth, and lift-off value, the depth is converted into theeffective permeability change using the correlation curve and used todetermine the corresponding total effective permeability for an infinitehalf-space of material associated with that notch depth. This totaleffective permeability is then used with the unflawed infinitehalf-space model to determine the effective sensor response to thisnotch depth. This process is repeated until the entire range of eachparameter (baseline permeability, depth, and lift-off) is covered. Asmentioned above, this process can be extended to include sensororientation and baseline lift-off as well.

FIG. 61 shows representative scan images of the effective permeabilityover the surface of the pipe and the depth estimate image. Note that theeffective permeability is the same as the absolute permeability far awayfrom the notches since uniform layer model used to generate thepermeability/lift-off grids apply in these regions. In some embodimentsthe color scale for the depth estimate image is chosen so that small (ornegative) depths that result from application of the algorithm tounflawed areas that may have slight material property variations will beappear in the background color for the image. The intensity of theselected color, such as blue or grey scale, in the image increases withthe observed depth and regions with responses deeper than the thresholdvalue, which in this case is 0.200 in., appear in a second color, suchas red or white. Note that similar results are obtained when all of thefrequencies (10, 40, 63, and 100 kHz) are used simultaneously toestimate the crack depths or when individual frequencies are used.

Section E-H: Further Applications

In some embodiments the impedance instrument and probe electronics unitmodule that are combined to reduce complexity, use low power consumingcomponents, use two or fewer simultaneous frequencies. This may beaccomplished to minimize power consumption and eliminate the need forfans so the tool can operate in difficult environments. The impedanceinstrument and probe electronics provide current at at least oneprescribed frequency to drive a linear segment of at least one driveconductor. The impedance instrument supports and probe electronicsprovide capability to simultaneously measure impedance for each of atleast two sensing elements, where the components of the impedance aremeasured simultaneously at the at least one frequency. The cable fromthe probe electronics to the sensor provides for the at least one drivecurrent and return, and said cable supports fully parallel voltagemeasurement for each of the at least two sensing elements. High dataresolution is achieved as compared to the frequency with filtering closeto the sensor.

The impedance instrument and probe electronics may be housed within ahousing and the cables to the sensors may support an eddy current arraythat is used to scan the inside of a pipeline. The sensor array responseat a plurality of sensing elements is used to determine the longitudinalstress on the internal surface of the pipeline using a drive conductorthat is aligned in the circumferential direction. The sensor arrayresponse at a plurality of sensing elements may be used to detect cracksinitiating from the internal surface of the pipeline. The sensor arrayresponse at a plurality of sensing elements is used to detect corrosionwall loss on the internal surface of the pipeline. The sensor arrayresponse may be used to measure mechanical damage in the pipeline, toassess weld related conditions in a pipeline, to determine if PWHT wasperformed properly, to detect cracks at seam welds initiating from theinternal surface of the pipeline, to detect cracks at girth weldsinitiating from the internal surface of the pipeline

The impedance instrument may be separated from a probe electronics unitmodule, where the probe electronics unit is attached directly to asensor with no cable length between them, and where the impedanceinstrument and probe electronics provide current at at least oneprescribed frequency to drive a linear segment of at least one driveconductor, and the impedance instrument supports and probe electronicsprovide capability to simultaneously measure impedance for each of atleast two sensing elements, where the components of the impedance aremeasured simultaneously at the at least one frequency.

A cable from the probe electronics to the sensor provides for at leastone drive current and return, and said cable supports fully parallelvoltage measurement for each of the at least two sensing elements.

The sensor may be flexible and have two rectangular drive conductorswith at least one linear array of MR sensing elements located at themid-point of one of the two rectangles. A precomputed database of sensorresponses may be used to detect external and internal corrosion in apipeline through insulation and metallic weather jacket, by estimatingthe lift-off, conductivity-thickness product, insulation thickness andpipeline wall thickness, using at least two frequencies. The weatherjacket overlap may be accounted for using a database of responses toimprove the capability to detect damage under the overlap. A stationarymeasurement is made at a location that does not have corrosion toestimate the conductivity of the pipe given an assumed nominal wallthickness, where the conductivity is then used to estimate wallthickness and detect and size corrosion damage for the rest of the pipesegment. The response at locations on the pipeline that do not appear tohave corrosion is used with an assumed nominal wall thickness toestimate the average nominal conductivity of the pipe segment and thisconductivity is used at other locations to detect and size corrosionrelated wall loss and to estimate confidence in the detection and sizingcapability. The sensor may be flexible and have at least one rectangulardrive conductors with at least one linear array of MR sensing elementslocated at the mid-point of the rectangular drive. A second array ofsensing elements is located at the mid-point of the second rectangle.The sensor response at a plurality of sensing elements may be used todetect damage. The sensor response is used to provide an estimate of thedamage size using a correlation relationship determined separately. Thedamage may be mechanical damage and the lift-off may be used to providea geometric measure of a mechanical damage profile and the magneticpermeability is used to assess the stress at the dent. The damage may bemechanical damage and the lift-off is used to provide a geometricmeasure of a mechanical damage profile and the magnetic permeability isused to detect cracks. The sensor response may be used to estimate themagnetic permeability and the magnetic permeability variation is used todetect hard spots. The sensing elements may be inductive. The sensingelements may be magnetoresistive. Though, there may be other sensingelement types.

The system may be used to inspect risers on an offshore platform, aboveor below water.

The data rate and channel count may be constrained in some embodiments.Exceeding the constrained number of channels may be achieved by stackingsystems. Power may be divided between the excitation frequencies in anysuitable way.

In some embodiments, sensor are permanently installed for fatigue andtorque measurement. In some embodiments, the sensor response is used toanalyze a fluid flowing within a pipe. In some embodiments, the pipe isplastic and the fluid is petrochemical in nature. In some embodiments,the sensor response is used to measure moisture in oil.

The sensor may be mounted on a mechanical scanner for inspection of apart from one side through a gap that is filled with a good insulator.In some embodiments, the good insulator layer is comprised of a layer ofair and a coating layer. Two frequencies may be used, where onefrequency is high enough that it does not substantially penetratethrough the pipe wall and one frequency is low enough that it doessubstantially penetrate through the pipe wall, where the data samplingrate is substantially higher than the lower frequency, where the higherresolution data is used to detect changes in the pipe condition thathave a smaller dimension than the distance traveled by the tool duringone period of the lower frequency response. Two frequencies responsesmay be used to measure the wall thickness and to detect anomalies thatcorrespond to wall thinning. The two frequency responses may be used todetect cracks in the pipe. Higher resolution data may be filtered toprovide an estimate of the size of a local damage anomaly.

An apparatus as in 1 where the sensor response is used to characterize athin conducting layer by utilizing the phase measurement resolution todiscriminate different layer conditions, where the skin depth is largerthan the layer thickness and the conductivity thickness product of thelayers produce is low enough to produce a phase of less than 1 degree.

Having thus described several aspects of at least one embodiment of thisinvention, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those skilled inthe art.

Such alterations, modifications, and improvements are intended to bepart of this disclosure, and are intended to be within the spirit andscope of the invention. Accordingly, the foregoing description anddrawings are by way of example only.

The above-described embodiments of the present invention can beimplemented in any of numerous ways. For example, the embodiments may beimplemented using hardware, software or a combination thereof. Whenimplemented in software, the software code can be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers.

Further, it should be appreciated that a computer may be embodied in anyof a number of forms, such as a rack-mounted computer, a desktopcomputer, a laptop computer, or a tablet computer. Additionally, acomputer may be embedded in a device not generally regarded as acomputer but with suitable processing capabilities, including a PersonalDigital Assistant (PDA), a smart phone or any other suitable portable orfixed electronic device.

Also, a computer may have one or more input and output devices. Thesedevices can be used, among other things, to present a user interface.Examples of output devices that can be used to provide a user interfaceinclude printers or display screens for visual presentation of outputand speakers or other sound generating devices for audible presentationof output. Examples of input devices that can be used for a userinterface include keyboards, and pointing devices, such as mice, touchpads, and digitizing tablets. As another example, a computer may receiveinput information through speech recognition or in other audible format.

Such computers may be interconnected by one or more networks in anysuitable form, including as a local area network or a wide area network,such as an enterprise network or the Internet. Such networks may bebased on any suitable technology and may operate according to anysuitable protocol and may include wireless networks, wired networks orfiber optic networks.

Also, the various methods or processes outlined herein may be coded assoftware that is executable on one or more processors that employ anyone of a variety of operating systems or platforms. Additionally, suchsoftware may be written using any of a number of suitable programminglanguages and/or programming or scripting tools, and also may becompiled as executable machine language code or intermediate code thatis executed on a framework or virtual machine.

In this respect, the invention may be embodied as a computer readablemedium (or multiple computer readable media) (e.g., a computer memory,one or more floppy discs, compact discs, optical discs, magnetic tapes,flash memories, circuit configurations in Field Programmable Gate Arraysor other semiconductor devices, or other tangible computer storagemedium) encoded with one or more programs that, when executed on one ormore computers or other processors, perform methods that implement thevarious embodiments of the invention discussed above. The computerreadable medium or media can be transportable, such that the program orprograms stored thereon can be loaded onto one or more differentcomputers or other processors to implement various aspects of thepresent invention as discussed above.

In this respect, it should be appreciated that one implementation of theabove-described embodiments comprises at least one computer-readablemedium encoded with a computer program (e.g., a plurality ofinstructions), which, when executed on a processor, performs some or allof the above-discussed functions of these embodiments. As used herein,the term “computer-readable medium” encompasses only a computer-readablemedium that can be considered to be a machine or a manufacture (i.e.,article of manufacture). A computer-readable medium may be, for example,a tangible medium on which computer-readable information may be encodedor stored, a storage medium on which computer-readable information maybe encoded or stored, and/or a non-transitory medium on whichcomputer-readable information may be encoded or stored. Othernon-exhaustive examples of computer-readable media include a computermemory (e.g., a ROM, a RAM, a flash memory, or other type of computermemory), a magnetic disc or tape, an optical disc, and/or other types ofcomputer-readable media that can be considered to be a machine or amanufacture.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects of the present invention asdiscussed above. Additionally, it should be appreciated that accordingto one aspect of this embodiment, one or more computer programs thatwhen executed perform methods of the present invention need not resideon a single computer or processor, but may be distributed in a modularfashion amongst a number of different computers or processors toimplement various aspects of the present invention.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, data structures may be stored in computer-readable media in anysuitable form. For simplicity of illustration, data structures may beshown to have fields that are related through location in the datastructure. Such relationships may likewise be achieved by assigningstorage for the fields with locations in a computer-readable medium thatconveys relationship between the fields. However, any suitable mechanismmay be used to establish a relationship between information in fields ofa data structure, including through the use of pointers, tags or othermechanisms that establish relationship between data elements.

Various aspects of the present invention may be used alone, incombination, or in a variety of arrangements not specifically discussedin the embodiments described in the foregoing and is therefore notlimited in its application to the details and arrangement of componentsset forth in the foregoing description or illustrated in the drawings.For example, aspects described in one embodiment may be combined in anymanner with aspects described in other embodiments.

Also, the invention may be embodied as a method, of which an example hasbeen provided. The acts performed as part of the method may be orderedin any suitable way. Accordingly, embodiments may be constructed inwhich acts are performed in an order different than illustrated, whichmay include performing some acts simultaneously, even though shown assequential acts in illustrative embodiments.

Use of ordinal terms such as “first,” “second,” “third,” etc., in theclaims to modify a claim element does not by itself connote anypriority, precedence, or order of one claim element over another or thetemporal order in which acts of a method are performed, but are usedmerely as labels to distinguish one claim element having a certain namefrom another element having a same name (but for use of the ordinalterm) to distinguish the claim elements.

Also, the phraseology and terminology used herein is for the purpose ofdescription and should not be regarded as limiting. The use of“including,” “comprising,” or “having,” “containing,” “involving,” andvariations thereof herein, is meant to encompass the items listedthereafter and equivalents thereof as well as additional items.

What is claimed is:
 1. An impedance instrument comprising: a signalgenerator configured to generate an in-phase reference signal, aquadrature reference signal, and an electrical signal oscillating at afirst excitation frequency, wherein the in-phase reference signal is adigital precursor to the electrical signal, and the quadrature referencesignal is a version of the in-phase reference signal shifted one-quarterperiod; and a sensing channel, the sensing channel having ananalog-to-digital converter to digitize a response signal into n (aninteger number) successive digitized samples and a multiply/accumulatemodule to process the n successive digitized samples with each of thein-phase and quadrature reference signals, to produce an impedancemeasurement, wherein the multiply/accumulate module separatelymultiplies the n successive digitized samples by respective samples ofrespective reference signals, separately adds products of the multiplyassociated with each reference signal, and divide each total by n toproduce a complex impedance measurement.
 2. The impedance instrument ofclaim 1, wherein the in-phase reference signal has a same phase as theelectrical signal.
 3. The impedance instrument of claim 1, wherein thesensing channel is among a plurality of parallel sensing channels eachhaving a respective multiply/accumulate module configured tosimultaneously process a respective digitized response signal with thein-phase reference signal and quadrature reference signal.
 4. Theimpedance instrument of claim 1, wherein the multiply/accumulate moduleof the sensing channel is implemented as a field-programmable gate array(FPGA).
 5. The impedance instrument of claim 1, wherein: the in-phasereference signal is a first in-phase reference signal, the quadraturereference signal is a first quadrature reference signal, and the signalgenerator is further configured to generate the electrical signal suchthat the electrical signal additionally oscillates at a secondexcitation frequency and to generate second in-phase and quadraturereference signals at the second frequency.
 6. The impedance instrumentof claim 5, further comprising a combiner module configured to add thefirst and second in-phase reference signal into a single combiner outputsignal.
 7. The impedance instrument of claim 6, wherein the combinermodule is further configured to apply a separate weight to the first andsecond in-phase reference signals before adding.
 8. The impedanceinstrument of claim 1 further comprising: a non-transient computerstorage medium storing a database of precomputed impedances for a sensorand test object; and a processor configured to receive the impedancemeasurement from the sensing channel and process the impedance with thedatabase to determine a property of the test object.
 9. The impedanceinstrument of claim 1, wherein n is a power of
 2. 10. The impedanceinstrument of claim 1, wherein the in-phase reference signal and thesuccessive digitized samples of the response signal have a samplefrequency f that is n times the excitation frequency.
 11. A method ofmeasuring impedance, the method comprising: generating a digital,in-phase reference signal and a digital, quadrature reference signal,the quadrature reference signal is a version of the in-phase referencesignal shifted one-quarter period; providing an electrical signaloscillating at a first frequency to a device having two or more ports,the electrical signal having been generated based on the in-phasereference signal; digitizing a response signal from the device into nsuccessive digitized samples; processing the n successive digitizedsamples of the response signal with the in-phase reference signal andthe quadrature reference signal to measure first and second componentsof the impedance, wherein the processing comprises multiplying the nsuccessive digitized samples by respective samples of respectivereference signals, separately adding products of the multiply associatedwith each reference signal, and dividing each total by n; and providingthe first and second component of the impedance as a representation ofthe impedance of the device.
 12. The method of claim 11, wherein thedevice is a sensor.
 13. The method of claim 12, wherein the device is aneddy-current sensor.
 14. The method of claim 12, wherein the device isan magnetoresistive sensor.
 15. The method of claim 11, whereinimpedance is represented in complex form having a real and an imaginarypart, and the first component of the impedance is the real part, and thesecond component of the impedance is the imaginary part.
 16. Ameasurement system comprising: a signal generator configured to generatean in-phase reference signal, a quadrature reference signal, and anelectrical signal oscillating at a first excitation frequency, whereinthe in-phase reference signal is a digital precursor to the electricalsignal, and the quadrature reference signal is a version of the in-phasereference signal shifted one-quarter period; and a plurality of sensingchannels, each sensing channel having an analog-to-digital converter todigitize a respective response signal into n (an integer number)successive digitized samples and a multiply/accumulate module having anin-phase path and a quadrature path, the in-phase path configured tomultiply the n successive digitized samples by respective samples of thein-phase reference signal to produce a first n products, sum the first nproducts into a first sum, and divide the first sum by n to produce afirst part of a complex impedance for the sensing channel, and thequadrature path configured to multiply the n successive digitizedsamples by respective samples of the quadrature reference signal toproduce a second n products, sum the second n products into a secondsum, and divide the second sum by n to produce a second part of acomplex impedance for the sensing channel.
 17. The measurement system ofclaim 16, wherein n is a power of
 2. 18. The measurement system of claim17, wherein the in-phase reference signal, the quadrature referencesignal, and the successive digitized samples for each response signalhave a sample frequency f_(c) that is n times the excitation frequency.19. The measurement system of claim 16, further comprises a sensorhaving a drive element and a plurality of sense elements, the driveelement electrically connected to the signal generator to receive theelectrical signal and the plurality of sense elements electricallyconnected to respective members of the plurality of sensing channels toprovide the respective response signals.
 20. The measurement system ofclaim 19, wherein the sensor is an eddy current sensor and the driveelement is a drive winding and the plurality of sense elements are sensewindings.